Arsenals France striker Giroud,who had not scored in all competitions since Nov. 23,got the faintest of touches to glance a Theo Walcott free kick into the net midway through the second half.
Arsenal top the table with 42 points from 19 games,one clear of Manchester City with Chelsea a point further adrift in third.
Chelsea heaped more Christmas misery on Liverpool with a 2-1 victory at Stamford Bridge and Olivier Giroud ended a seven-game scoring drought to help Arsenal win 1-0 at Newcastle United and return to the top of the Premier League on Sunday.
Everton moved back into the top four with a 2-1 win over Southampton and Tottenham Hotspur beat Stoke City 3-0 to get their first victory since appointing Tim Sherwood as permanent manager.
Chelsea fell behind to a goal from Martin Skrtel after four minutes,but rallied with first-half strikes from Eden Hazard and Samuel Etoo to inflict a second defeat in four days on Liverpool,who lost to Manchester City on Thursday.
Liverpool,who topped the table on Christmas Day,dropped to fifth,a point behind local rivals Everton who moved fourth with 37 points thanks to a second-half winner from Romelu Lukaku.
The Belgian,who had not scored for Everton in five games,struck three minutes after Gaston Ramirez cancelled out Seamus Colemans early opener.
A Roberto Soldado penalty and goals from Mousa Dembele and Aaron Lennon lifted Tottenham go seventh on 34 points.
Arsenal kept possession neatly,but without injured playmaker Mesut Ozil,lacked incision and failed to create a chance of note in the first half.
It looked to be heading towards a draw when Arsenal struck the decisive blow. Walcotts free kick was perfectly angled into the box and Giroud got in between the Newcastle centre backs to feather a delicate header into the net.
It could have been 2-0 moments later but Walcott missed two chances to put the game to bed,with Newcastle keeper Tim Krul saving his first shot while his follow-up effort was cleared off the line by Mathieu Debuchy.
There was a frenetic finale but Arsenals defence held out to ensure they go into the New Year on top of the table for the first time since 2007-08,to provide manager Arsene Wenger with some festive cheer.