|Luiz Suarez (C) clashes with Chelsea's English defender Gary Cahill (R). Photo: AFP|
Arsene Wenger's side had surrendered first place after Manchester City's win over Crystal Palace on Saturday, but just 24 hours later the Gunners reclaimed pole position with a hard-fought victory at St James' Park.
Giroud's first goal since November 23 was enough to give Arsenal their second successive win and move them one point ahead of second placed City heading into the new year.
Arsenal, who were without German playmaker Mesut Ozil, took the lead when France forward Giroud bagged his 11th goal of the season with a glancing header from Theo Walcott's free-kick in the 65th minute.
"There is a big satisfaction because we surprised many people," Wenger said.
"We played two away games and got six points against West Ham and Newcastle and as you can see the team is ready for a fight.
"Ozil has a shoulder problem. I don't think he will be available for Cardiff on Wednesday, maybe after that, we will see."
At Stamford Bridge, Chelsea came from behind to win the weekend's marquee match-up thanks to goals from Eden Hazard and Samuel Eto'o.
Jose Mourinho's third-placed team are now two points adrift of Arsenal and one behind City, with Liverpool slipping down to fifth spot.
Liverpool had made a dream start when Martin Skrtel bundled home from close-range after Chelsea failed to clear Phillipe Coutinho's inswinging free-kick.
But Brendan Rodgers' side also took the lead and still lost at Manchester City on Boxing Day and once again they were unable to hold onto their advantage.
It took the Blues just 14 minutes to equalise as Oscar's shot hit Mamadou Sakho and bounced towards Belgian midfielder Hazard, who seized possession and blasted an unstoppable shot into the top corner of Simon Mignolet's goal.
And Chelsea struck again in the 34th minute when Cameroon striker Samuel Eto'o met Oscar's low cross with a prodded strike that eluded Mignolet's weak attempted save.
Liverpool twice appealed in vain for a penalty when Luis Suarez went down under challenges from John Terry and then Eto'o and the Reds were unable to avoid a second successive defeat.
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