Frank Lampard side Chelsea has beaten Tottenham at the Stamford Bridge to go four points clear.
An early first half goal from Giroud gave Lampard a reason to smile in one of the toughest English Premier League fixtures.
Alonso doubled the lead three minutes after the start of the second half to the surprise of Jose Mourinho.
One minute left to the end of the normal 90 minutes, Rudiger scored an own goal but it was too late for Tottenham to bounce back.
The win leaves Lampard at position our with 44 points as Mourinho trails behind him with 40 points.
Tottenham was expected to be shaky as they missed crucial services of Harry Kane and Son Heung who are nursing muscle and arm injuries respectively.
Both teams came into match having lost their previous matches against Manchester United and Leipzing during the EPL and Champions League fixtures.
The Blue were beaten two goals to nill at the Stamford Bridge as Tottenham were hammered a solitary goal at home in the Champions League.