Ramsey finished from close range in the first minute of stoppage time to complete Arsenal's comeback against a stingy Crystal Palace, who had led through Brede Hangeland's first-half header. Laurent Koscielny equalised for the Gunners late in the first half.
Arsenal generally struggled to break down Crystal Palace's stubborn, organised defending but eventually won after converting twice from set pieces. This was the club's first opening-day win since 2009.
Palace finished the match with 10 men after Jason Puncheon was sent off in the 89th minute for his second bookable offence.
Arsenal entered the match riding high expectations after signing Chilean forward Alexis Sanchez in the summer. In addition, the Gunners brought in defenders Mathieu Debuchy and Calum Chambers, both of whom started a week after the confidence-boosting victory over champions Manchester City in the Community Shield.
Saturday's result was exactly what Arsenal wanted, and hopes will remain high in north London following last season's FA Cup triumph and fourth-place league finish. But manager Arsene Wenger will hope his side can break down opponents more quickly in the coming weeks, as the Gunners face a tricky run of games.
Regardless of how those matches play out, Arsenal might yet conduct more business in the transfer market. According to the Metro, Wenger is in the market for a defensive midfielder able to play centre-back as well. In addition, ESPN have linked Arsenal with Olympiakos centre-back Kostas Manolas.
Crystal Palace, meanwhile, face an uncertain future following the unexpected departure of manager Tony Pulis on Thursday, less than 24 hours before Saturday's kick-off. In an official statement, the club announced that the decision had been reached by "mutual consent," while multiple media reports, including ones from The Mirror and the BBC, claimed Pulis had disagreed with co-chairman Steve Parish over transfers.
Palace host West Ham United next Saturday.
Arsenal dominated the ball in the early stages but failed to register a shot on target until 29th minute, when Jack Wilshere's bouncing shot was saved comfortably by Julian Speroni. But for all of Arsenal's possession, it was Crystal Palace who went ahead in the 35th minute. Puncheon curled in a corner from the right, and Hangeland rose highest to flick a simple header in at the far post.
But the Gunners erased the deficit quickly. Koscielny, who was partially to blame for Palace's opener, made amends at the other end in the first minute of stoppage time with the equaliser. Alexis served as provider, floating a free-kick into the box for Koscielny, who showed excellent body control to head in a tough chance.
After heading into the break on level terms, Arsenal made the game's first substitution in the 53rd, introducing full-back Nacho Monreal in place of Kieran Gibbs, who appeared to have sustained a minor injury.
The hosts piled on the pressure but continued to struggle in breaking down Palace. Sanchez managed to shoot on target in the 68th minute following fine interplay in midfield, but his effort lacked power and Speroni saved easily. Four minutes later, the Palace goalkeeper comfortably collected Aaron Ramsey's curling strike as well.
When substitute Olivier Giroud flashed a cross-shot across the face of goal in the 84th minute, Arsenal appeared on course for a frustrating draw. But the Gunners' fortunes started to turn around when Puncheon received his marching orders one minute from time after seeing his second yellow card.
Then Ramsey popped up with the winning goal in the first minute of stoppage time. The goal came from another set piece, Palace failing to properly clear a corner. Giroud headed down in front of goal for Debuchy, whose close-range shot was blocked. But Ramsey was on hand to turn in the rebound and start the celebration among the Emirates Stadium faithful.
|Arsenal Player Ratings|
|Nacho Monreal (for Gibbs, 53')||6.6|
|Olivier Giroud (for Sanogo, 62')||6.3|
|Alex Oxlade-Chamberlain (for WIlshere, 69')||6.2|
|Ratings via WhoScored.com|
|Crystal Palace Player Ratings|
|Damien Delaney (for Dann, 75')||6.0|
|Dwight Gayle (for Campbell, 85')||No rating|
|Stuart O'Keefe (for Bolasie, 90')||No rating|
|Ratings via WhoScored.com|
Wenger said Crystal Palace made Arsenal's task difficult, telling Arsenal.com:
(Needing a late winner) was not the plan; the plan was to win the game, but because of the physicality and organisation level of Crystal Palace, it was very difficult for us. Why? Because we conceded a goal on the first corner they had. We lacked a bit of pace in the final third to change what we built up into dangerous situations.
But it was enough to win the game and win the three points. You could see that for the first game of the season, nobody won at home, we were the only team that won at home. So that shows you that it's difficult for everybody on the first day of the season. We got the three points we wanted, now let's focus on Besiktas.
Interim manager Keith Millen expressed pride in the performance of Crystal Palace's players, telling BBC Sport:
I'm proud of the players, without a doubt. I'm proud of the performance and disappointed not to have got something out of the game.
That's the only disappointment really today, the two goals and the timing of the goals. But, I think when you think what the players have been through the last couple of days, you're never quite sure how they're going to respond to Tony (Pulis) leaving.
I think you can see by their performance, their togetherness, that they were going to work hard for each other and the club.