Arsene Wenger's men were sternly tested by a Newcastle side harbouring UEFA 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 defence allowed Giroud the space to glance home the winner after 65 minutes.
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, Arsenal holding on to stretch their unbeaten league run on Tyneside to seven matches.
Arsenal enjoyed the lion's share of possession in the early stages, but it took over 20 minutes to craft the game's first real opportunity as Jack Wilshere fired over the crossbar from long range.
Newcastle full-back Mathieu Debuchy then went close with a half-volley at the near post before team-mate Tim Krul was forced into the first save of the match from Tomas Rosicky's drive.
Newcastle carried that momentum into the second half and would have taken the lead had Yoan Gouffran been able to capitalise on a mix-up in the Arsenal defence caused by Vurnon Anita's right-wing cross seven minutes into the second period.
Arsenal struggled to break down a well-organised defence for much of the encounter. However, after 65 minutes the visitors did break 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.
