Mesut Ozil had a shot back-heeled off the line by Gary Cahill while Chelsea had an awesome escape when Danny Welbeck's header thumped against the post and Ramsey bundled the ball back against the same upright.
Chelsea improved after the break but had to play the final quarter of the match with 10 men after Victor Moses received his second yellow card following a blatant dive in the area.
Bellerin shot just wide and Ozil hit the post after cutting inside Cesar Azpilicueta, but just as in the 2014 final against Hull City, Ramsey's goal was to prove the victor.
Ospina then atoned for Costa's goal by producing a fine save to deny the Spain striker, and Ozil hit the post late on.
"But once the game starts and you are a fan, you stand behind the team, that is what I have not accepted this season and I will never accept it". The German defender put in a dominant display to keep Costa quiet.
"I've been on the receiving end of losing Cup finals and it's not a nice feeling on the last day of the season". "It would be a bit ridiculous that 20 years depends on one games and the future of the club depends on one games, we will see more next week".
A piece of unwanted history for the Chelsea player.
Whatever the future holds for Wenger, he said the current Arsenal team can look forward with optimism.
Mertesacker was playing alongside a left-back Nacho Monreal who was converted to centre-back, while youngster Rob Holding was playing in his first major showpiece.
Arsenal. Chelsea. Two names that embody the idea of British soccer.
Chelsea had been hot favourites to complete a remarkable debut season for manager Antonio Conte but were not at their clinical best as Arsenal, who finished fifth in the league, lifted the Cup for the third time in four seasons.
They got off to the worst possible start, going behind after just four minutes.
The 32-year-old had played only 37 minutes all season after coming off the bench in last weekend's win against Everton.
Terry experienced his first FA Cup final as an unused substitute in Chelsea's win over Aston Villa in 2000. This aspect I can stay calm and I trust the players, it is impossible not to after this season .
Later on Sunday, Secretary of State Rex Tillerson told Fox News that North Korea nuclear testing was "disappointing, disturbing". South Korea says it has fired warning shots at an object that flew across the demilitarised zone from North Korea .
The previous year, many students and teachers said that components of the JEE (Advanced) were particularly challenging. The paper contained a mix of single choice, multiple correct choice and passage type single choice question.
Indian army Tuesday claimed it had damaged some Pakistani army posts on LoC and described it as "punitive fire assaults". Two groups of terrorists managed to cross the LoC even during winter when the mountain passes were covered with snow.
Trump has called the investigation of his presidential campaign's ties with Russian Federation a "witch hunt". The paper said the comments came from the White House's written account of the Oval Office meeting.
As I mentioned Memorial Day has the best chance (60%) for widespread showers and storms which could interrupt your holiday plans. Highs will pick up Tuesday , with high 60s to low 70s expected through Friday , when we should also see a gradual clearing.
A game of football or a concert is a moment that you must live with passion and enthusiasm. "I just want to enjoy my football". He can think what he wants. "For this reason, I hope to see a great game and all my players trying to win for us", Conte said.
Several key details about the investigation into the Manchester terrorist attack were leaked to the news media by USA officials. As the investigation continues, authorities have said that they are certain they now know the names of all the victims.
More than two thirds, 68 percent, said that Russian interference in the election is "very important" or "somewhat important". According to the survey, the president's job approval rating declined to 45 percent now from 49 percent in March.
Steven Mnuchin at G7: 'We don't want to be protectionist'
Another senior official from the delegation said, "Each one of us is following developments in USA tax policy very closely". The aim for the G7 and central bankers on Saturday is to join forces to fight the growing threat of worldwide cyber attacks.
With budget unfinished, Legislature heads to special session
There were other complications with the one-page special session agreement hurriedly drafted Monday among the state's top leaders. On Wednesday, the House approved bills for taxes, education and transportation, with senators doing the same with taxes.
'Foiling' America's Cup due to set sail Saturday in Bermuda
Showing all of his class and experience, Oracle skipper Jimmy Spithill refused to give in and gradually clawed his way back. Crewmen on SoftBank Team Japan had to leap clear of Ainslie's port hull as it crashed onto their starboard hull.
Exeter champions after extra-time win over Wasps
Short is Exeter's top try-scorer this season, scoring 11 tries in the Premiership and going over 14 times in all competitions. The game also marked England worldwide Danny Cipriani's return to Wasps after he rejoined from Sale Sharks over the summer.
Next stop for Trump is Israel, in pursuit of 'ultimate deal'
Trump is expected to become the first sitting U.S. president to visit the Western Wall , the holiest site where Jews can pray. His nine-day trip through the Middle East and Europe ends on Saturday after visits to the Vatican, Brussels and Sicily.
A Warm Memorial Day Weekend, Could See Some Rain
MEMORIAL DAY MONDAY: Partly cloudy skies will develop for Memorial Day Monday, with a high temperature of 79 degrees. New rainfall amounts between a tenth and quarter of an inch, except for higher amounts possible in thunderstorms.
British police say military to guard key London sites
Sixty-four people are still hospitalized, Jon Rouse of the Greater Manchester Health and Social Care Partnership said Wednesday. France, which has repeatedly been hit by devastating militant attacks since 2015, extended emergency powers.
China Hit With First Credit Downgrade In Decades
The Chinese finance ministry claimed Moody's had painted an inaccurate picture of the country's financial outlook. The downgrade adds to warnings about China's reliance on credit to propel growth after the 2008 global crisis.
China to address implementation of Paris Agreement
Taking into account the economic benefits of avoiding climate change impacts such as flooding, that number goes up to nearly . And the world's most vulnerable countries reminded us that no country can be "great" without increased climate action.
Saudi oil minister confident in extension of production cuts
It is far below cuts from OPEC at a time when demand is likely to keep growing strong, said Justin Jenkins, analyst at the firm. Non-OPEC nations Oman and Mexico also confirmed their support for prolonging the curbs through the first quarter of 2018.