Spurs' 100 per cent start to the season came to a grinding halt at the home of their fiercest rivals, with Andre Villas-Boas' expensively-assembled squad drawing a blank at Emirates Stadium.
It was the in-form Giroud who cut them down to size on Sunday, with the France international expertly turning home a low cross from Theo Walcott on 23 minutes - with Hugo Lloris beaten for pace at his near post.
There was a bright start by the hosts, and Santi Cazorla forced a fine early save from Hugo Lloris with a 20-yard curling free-kick.
The Spaniard then had another go from a more central position after Theo Walcott was upended by Mousa Dembele, and this time his low effort went under the wall, bobbling just wide.
Spurs settled and Roberto Soldado, the £26million striker signed from Valencia, had a close-range shot blocked by Per Mertesacker.
Arsenal, though, swept into the lead after 23 minutes, with a swift counter from Aaron Ramsey and Tomas Rosicky seeing the ball played out to Walcott down the right.
The England forward cut a pass towards the six-yard box - where Giroud arrived ahead of Spurs captain Michael Dawson at the near post to convert a lovely left-footed finish.
Arsenal looked to quickly further extend their advantage, with Walcott's angled drive beaten away by Lloris. Wales midfielder Aaron Ramsey then crashed a shot horribly over the bar after being set up just inside the area by Cazorla.
Lloris then came rushing out of his area to slide in on Walcott and got his toe to the ball as the Arsenal forward tumbled - with the home fans screaming for what could have been a red card from referee Michael Oliver, whose decision was backed up by television replays.
Arsenal were forced into a change just before half-time, when midfielder Jack Wilshere signalled he was unable to continue and hobbled off, to be replaced by Mathieu Flamini - the former Gunner rejoining his old club on a free earlier this week.
Spurs made a lively start to the second half, forcing a couple of corners from which they failed to really test the Arsenal defence.
Arsenal were struggling to find fluency, as the tempo was interrupted by a string of niggly fouls from both sides.
Spurs boss Andre Villas-Boas looked to liven up his attack with 20 minutes left as Dembele was replaced by Jermain Defoe.
Arsenal were the next to threaten, though, with Lloris racing out quickly to beat Walcott to the loose ball again, this time with his hands.
There was a stoppage as Tottenham midfielder Etienne Capoue - signed from Toulouse in a £9million deal - needed treatment after badly twisting his ankle in a tackle with Cazorla, and had to be carried off on a stretcher.
Spurs went close to an equaliser when Defoe's shot at the near post was saved by Wojciech Szczesny and the follow-up from Soldado cannoned into Giroud.
At the other end, Walcott's shot was saved by Lloris with substitute Nacho Monreal just unable to get to the rebound.
Spurs continued to push Arsenal back during five minutes of stoppage time, but Arsene Wenger's men remained resilient - and jubilant chants of 'What a waste of money' from the home fans followed the final whistle.