Giroud guides Chelsea closer to the Champions League
Olivier Giroud's header in first half stoppage time secured the Blues a much-needed three points with a trip to champions Liverpool and sixth-placed Wolves visiting Stamford Bridge on the last day of the season to come in Chelsea's final two league games of the season.
Leicester can narrow the gap when they host Sheffield United on Wednesday, while United travel to Crystal Palace on Thursday.
Frank Lampard was furious with his side's lack of fight in surrendering to a 3-0 defeat at Sheffield United on Saturday that plunged Chelsea's chances of a top-four finish into doubt.
Lampard made five changes from the battering at Bramall Lane with Giroud among those restored to the starting line-up.
Chelsea have already significantly bolstered their frontline for next season with the signings of Timo Werner and Hakim Ziyech.
But Giroud has more than justified the decision to also extend his contract by a year during football's shutdown as Chelsea's most potent striker since the restart.
The French World Cup winner saw a number of chances come and go in the first half as an attempted lob over Tim Krul fell gently into the Dutch 'keeper's arms before he sliced well over the bar when unmarked inside the area.
Christian Pulisic forced Krul into his best save of the first-half with a powerful drive that was just too close to the former Newcastle stopper.
Just as Norwich looked set to hold out until the break Giroud shrugged off Tim Klose to connect with Pulisic's cross for his fifth goal in eight games.
Norwich's long-awaited fate of a return to the Championship was confirmed in a 4-0 thrashing at the hands of West Ham on Saturday.
There was more defiance from the Canaries in defence, but they failed to score for the seventh time in their last eight games to slump to a ninth straight defeat.
Daniel Farke's men failed to even test Chelsea goalkeeper Kepa Arrizabalaga or a defence that has been under the microscope for conceding 49 goals already in the league this season.
Krul denied Pulisic again after the break and made a fine save from Willian's free-kick late on as Chelsea had to settle for a solitary goal.