Giroud made it 1-0 to Chelsea on 15 minutes when he reacted quickest to finish beyond Hugo Lloris after Ross Barkley had struck a post.
Chelsea doubled their advantage three minutes into the second half, Alonso drilling in a first-time shot after being set up by Barkley.
Spurs gave Chelsea a nervous ending after substitute Erik Lamela's shot went in off Antonio Rudiger in the 89th minute but could not find an equaliser.
A first win in five Premier League matches gives Frank Lampard's side 44 points.
Chelsea: 29 Feb v AFC Bournemouth (A)
Spurs: 1 Mar v Wolves (H)