Bielsa endured a disappointing start to his reign at the Stade Velodrome, his side giving up a two-goal lead to draw with Bastia before suffering a 2-0 home defeat at the hands of Montpellier.
However, victory at Guingamp last weekend provided Marseille with a welcome boost and they ran out convincing winners against Nice, with Payet and Florian Thauvin particularly influential.
Marseille duly seized control, Thauvin seeing a goalbound shot cleared away by a defender before doubling his side's lead on the stroke of half-time with a close-range finish from Andre Ayew's cutback.
A third goal arrived three minutes into the second half as Thauvin turned provider, providing the assist for Payet to find the net with a fine diving header.
Payet's second looked set to round off the scoring, but Abdelaziz Barrada added a fourth with three minutes remaining, the substitute converting a tap-in to claim his first goal for Marseille.
