The central defender prodded home from close range seven minutes after the break to ensure that the Gunners could not be overhauled by north London rivals Tottenham in the fight for fourth place in the Barclays Premier League.
But the result was in doubt until the final kick of the game, with Tottenham's home win over Sunderland meaning a late equaliser for Alan Pardew's men would have meant Spurs and not the Gunners getting a shot at Europe's premier club competition.
The Gunners enjoyed plenty of possession with Santi Cazorla the fulcrum, but with Newcastle defending competently, they found chances few and far between.
Theo Walcott, who was largely effectively contained by makeshift full-back Mapou Yanga-Mbiwa before the break, whistled a sixth-minute shot over Steve Harper's crossbar and Koscielny glanced a header harmlessly wide from Cazorla's 12th-minute corner.
But in the meantime, Magpies striker Papiss Cisse had gone significantly closer, whipping a first-time left-foot effort just over after a fine run and cross by Yanga-Mbiwa.
However, Arsenal had emerged in far more determined mood and they went ahead with 52 minutes played when Lukas Podolski headed down Walcott's free-kick for central defensive partner Koscielny to volley past the helpless Harper from close range.
It took Per Mertesacker's intervention to deny Yoan Gouffran a 64th-minute equaliser after Vurnon Anita had picked out Mathieu Debuchy on the right, and the Frenchman was soon replaced by compatriot Sylvain Marveaux as Pardew looked for a way back into the game.
Walcott had a glorious opportunity to make sure at the death when he carved his way through the home defence, but with just Harper to beat, he stabbed the ball against the foot of the far post, but ultimately Koscielny's effort proved enough.
Source: PA
Source: PA