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.
Nice started brightly, but fell behind in the 19th minute when Payet fired home after an initial effort had been blocked.
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.
'Obviously Messi is the best player in history and being compared to him means that you're doing things right, but I try to be myself': Barcelona star responds to comparisons with Argentine legend
'Darwin Nunez would be gold for Arsenal': Liverpool legend claims Gunners should have signed Uruguayan striker in January
