Ramsey, whose goal won the FA Cup at Wembley in May, smashed the ball home from close range as the Gunners came from behind to win their Barclays Premier League opener 2-1 at the Emirates Stadium.
Defeat was harsh on the Eagles, who had produced a determined display at the end of a difficult few days following the shock departure of manager Tony Pulis on the eve of the new season.
Indeed, a first-half header from Brede Hangeland, one of the few summer signings sanctioned by chairman Steve Parish, had put the hard-working Eagles ahead.
Laurent Koscielny flicked home a free-kick from £30million Chile forward Alexis Sanchez to level before the break.
Arsenal lacked a cutting edge in the final third, creating only a few half-chances before Ramsey was on hand to slot home after Mathieu Debuchy's shot was saved - after Jason Puncheon had been sent off for a second yellow card.
It had earlier been a positive start by the Gunners, who were without World Cup winning trio Mesut Ozil, Per Mertesacker and Lukas Podolski, all unlikely to be involved until after the midweek Champions League play-off away to Beskitas.
Sanchez, signed from Barcelona, tried his luck when the ball broke to him some 25 yards out, but the Chilean's long-range chip over Julian Speroni drifted well wide.
The Palace goalkeeper had to be alert on 29 minutes to get down quickly and push a low, curling 18-yard shot from Jack Wilshere behind.
There was a rare moment of panic in the Arsenal rearguard when Wojciech Szczesny's scuffed clearance was driven back towards goal from the halfway line by Marouane Chamakh.
Koscielny was able to get across and block, before Fraizer Campbell's follow-up was put behind.
From the corner, Palace took the lead on 35 minutes
Puncheon floated the corner in from the right, where Hangeland flicked it on at the near post into the far corner
After being hit against the run of play, Arsenal needed to regroup quickly, and did so as Koscielny levelled just before half-time.
Sanchez was fouled some 35 yards out, and floated a deep free-kick over the Palace defence.
Koscielny ghosted behind the wall of yellow shirts and flicked the ball off the back of his neck into the corner.
Arsenal were forced into a change just after the start of the second half when full-back Kieran Gibbs pulled up with what looked like a hamstring problem and was replaced by Nacho Monreal.
Palace continued to prove difficult to break down, which had been a trademark of Pulis' reign, but also looked dangerous on the counter.
On the hour mark, Sanogo was replaced by Olivier Giroud, the France international having come off the bench at Wembley last weekend to crack home a superb third goal in the Community Shield win over Manchester City.
Arsenal appealed for a penalty when the ball bounced onto Chamakh's arm and chest, but the referee was unmoved.
Chamakh, who had committed a string of fouls all afternoon, was then finally shown a yellow card for clattering into Wilshere on the halfway line.
The midfielder was soon replaced, perhaps as a precaution, by England team-mate Alex Oxlade-Chamberlain with 20 minutes left.
Arsenal had another penalty claim turned away by Moss when Giroud looked to have been pulled down by Hangeland as the ball was swung in from Sanchez.
Giroud flashed an angled drive across the face of goal before, with two minutes left, Puncheon was sent off for a second caution after a late challenge on Monreal.
Arsenal continued to press and were rewarded in the closing moments.
Giroud's knockdown was fired goalwards by Debuchy, signed from Newcastle, and although Speroni produced a fine reaction stop at point-blank range, Ramsey was alert to smash in the rebound and send the Emirates Stadium faithful into wild celebration.
Source : PA