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The Gunners began well and came close with to scoring from two early Santi Cazorla free kicks. The first was pushed away from goal by a sprawling Hugo Lloris and Cazorla cleverly side-footed his second under the jumping Spurs wall and inches wide of the post with Lloris rooted.
Tottenham's first decent sight of goal came when Kyle Walker burst down the right and pulled it back for Roberto Soldado, whose swipe at goal was blocked.
Arsenal took the lead bang on the midway point of the half when Michael Dawson played Theo Walcott onside and the England international crossed for Giroud, who nipped in ahead of the Spurs defender to flick home past Lloris at the near post.
Moments later it was almost 2-0 as Aaron Ramsey played in Walcott down the right and the winger shot low from a tight angle, with Lloris turning it away.
Wojciech Szczesny was called into action for the first time when Andros Townsend cut in from the right and fired at the near post on the half-hour mark.
Arsenal went down the other end and perhaps should have doubled their lead, but Ramsey blazed his shot high over the crossbar.
Chances were coming thick and fast and next to have an opening was Walcott, who raced in on goal but was expertly tackled by a sliding Lloris.
With the half coming to a close, Gunners manager Arsene Wenger was forced into an early change as Mathieu Flamini made his second debut for the club by replacing Jack Wilshere, who may now miss the upcoming England qualifiers against Moldova and Ukraine because of injury.
Follow live coverage of the second half at the Emirates Stadium by clicking here.