The Frenchman got the last touch on Theo Walcott's delivery to secure a slightly nervy three points at St. James's Park that took his side back above Manchester City.
Arsene Wenger's men were sternly tested by a Newcastle side with Champions League ambitions but they did enough to take the points in an encounter largely devoid of goalscoring opportunities.
The hosts created the better chances for much of the contest but a lapse in concentration in defense allowed Giroud the space to glance home the winner after 65 minutes.
The France international got the faintest of touches to head home his first goal since his double against Southampton in November, sending Arsenal back to the summit.
Alan Pardew's men failed to mount a meaningful response, although Loic Remy almost took advantage of an error from Wojciech Szczesny in the closing stages, with Arsenal holding on to stretch its unbeaten league run on Tyneside to seven matches.
Cheikh Tiote replaced Hatem Ben Arfa in the Newcastle starting XI after missing the win over Stoke City through suspension, while Laurent Koscielny returned to an Arsenal side that was missing the midfield talents of Mesut Ozil and Aaron Ramsey.
The north Londoners enjoyed the lion's share of possession in the early stages but it took more than 20 minutes to craft the game's first real opportunity as Jack Wilshere fired over the crossbar from long range.
Newcastle fullback Mathieu Debuchy then went close with a half-volley at the near post before teammate Tim Krul was forced into the first save of the match from Tomas Rosicky's drive.
The hosts finished the half the stronger as Moussa Sissoko forced a flying save from Szczesny, with Debuchy heading against the underside of the bar from the resulting corner.
Newcastle carried that momentum into the second half and would have taken the lead had Yoan Gouffran been able to capitalize on a mix-up in the Arsenal defense caused by Vurnon Anita's right-wing cross seven minutes into the second period.
The visitors struggled to break down a well-organized defense for much of the encounter. However, after 65 minutes, they broke the deadlock when Giroud flicked home Theo Walcott's free kick.
That goal provided Arsenal with added impetus and Wenger's men would have doubled their advantage had it not been for a piece of brilliant defending by Debuchy, who headed Walcott's goalbound effort off the line via the crossbar after Krul had kept out the England international's initial effort.
Arsenal defended its lead with relative comfort for the most part but its hard work was nearly undone by Szczesny, whose clearance struck the face of Remy eight minutes from time, only to trickle narrowly wide of the post.