Goalscoring opportunities were scarce throughout a testy encounter on Tyneside, but Giroud's first goal in over a month was enough to hand Arsenal a seventh away win of the season.
The first half was bereft of chances until added time when Mathieu Debuchy's looping header from a corner came back off the underside of the bar after Wojciech Szczesny had acrobatically tipped Moussa Sissoko's shot over.
The breakthrough went Arsenal's way on 65 minutes when Theo Walcott chipped a free-kick into the box and Giroud got ahead of his marker to guide a deft header beyond Tim Krul.
Just four minutes later, the same two players had a chance to double the lead when Walcott's lob from close range was cleared off the line by Debuchy, via the crossbar, but Giroud made a mess of the loose ball.
Arsenal gave themselves a scare with nine minutes to go when Szczesny's clearance smacked Loic Remy flush in the face before rolling wide of goal, but the visitors hung on to go back above Manchester City at the summit.
Newcastle boss Alan Pardew was able to draft Cheick Tiote back into his starting line-up after suspension with Hatem Ben Arfa making way, but opposite number Arsene Wenger was not so fortunate as he lost Mesut Ozil and Aaron Ramsey to injury, and Thomas Vermaelen and Nacho Monreal to illness.
Pardew, just as he had done in the 2-0 win over Chelsea in November, set out to frustrate the Gunners with a five-man midfield, but saw his side concede space and possession in the early stages as they found themselves pinned back.
However, for all they created half-chances, keeper Tim Krul did not have a save of note to make with Tomas Rosicky shooting straight at him from 20 yards with 27 minutes gone.
Santi Cazorla extended the Holland international three minutes later with a deflected effort which dipped nastily in front of him, but Giroud curled harmlessly wide 12 minutes before the break.
The Magpies had a chance to take a 12th-minute lead when Yohan Cabaye, who was a summer target for Arsenal, floated the ball over the top into Debuchy's run, but the defender could not control with just Szczesny to beat.
The Frenchman shot wide from a similar position 13 minutes later after again getting in round the back to collect Cabaye's deep free-kick, but he was to go significantly closer as the half-time whistle approached.
There was barely a minute of added time remaining when Vurnon Anita surged forward and picked out Cabaye, whose long-range strike was blocked by Laurent Koscielny, only for Sissoko to latch on to the rebound and force Szczesny to tip over a piledriver.
From the resulting corner, Debuchy headed against the underside of the crossbar and the Gunners managed to smuggle the loose ball away as referee Lee Probert blew for half-time.
After a tentative start to the second half, Anita caused panic in the Gunners' defence when he clipped a cross towards lone striker Remy, although between them Szczesny and his colleagues managed to keep the Frenchman at bay, if at full stretch.
Pardew made his move with 28 minutes remaining when he sent on Ben Arfa for the tiring Yoan Gouffran and charged him with the task of running at Arsenal.
But it was the visitors who went ahead three minutes later when Walcott floated a free-kick into the box and Giroud got ahead of Mike Williamson to glance it past Krul.
He should have doubled his tally within four minutes when, after Walcott saw his initial effort blocked by Krul and his follow-up headed off the line by Debuchy, the ball fell to him with the goal at his mercy, but he could not hit the target.
Newcastle pushed for a late equaliser and came close when Szczesny hammered the ball at Remy and looked on helplessly as it ran just wide.