PSG host relegation battling Le Havre on Saturday
Chelsea moved 12 points clear of their London rivals and the chasing pack with a dominant performance at Stamford Bridge.
Alonso outmuscled Hector Bellerin to head home in the 13th minute and early in second half Hazard picked up the ball just past the halfway line and shrugged off Francis Coquelin before rounding Laurent Koscielny and dodging Shkodran Mustafi to score.
Chelsea outplayed Arsenal, watched by their suspended manager Arsene Wenger from the stands, and goalkeeper Petr Cech gifted Fabregas the third when he failed to clear and the Spaniard lifted the ball into an empty net.
Arsenal substitute Olivier Giroud headed a consolation goal in stoppage time.