Marquez fractured his right arm when he fell in the first Grand Prix of last season, an injury that required three bouts of surgery, the last in December.
Spanish rookie Jorge Martin, the teammate of Zarco, was third after starting the race on pole position.
Francesco Bagnaia on another Ducati came third on his first ride in the factory team after starting on pole, beating reigning champion Joan Mir of Suzuki back into fourth in the final moments of the race
MotoGP 2021: Ducati's Francesco Bagnaia takes first pole of season in Qatar pipping Fabio Quartararo
Another Yamaha rider, Spaniard Maverick Vinales completed the front row after nudging out Italian veteran Valentino Rossi of Yamaha satellite team SRT, late in the session.
Dovizioso, who turns 35 on 23 March, began his career in 2000 racing 125cc bikes for Aprilia. He reached MotoGP in 2008 winning 15 races and finishing runner up in the championship for three straight seasons from 2017-19 with Ducati.
MotoGP 2021 season to begin with two races in Qatar, pre-season testing to commence in first week of March
The two night races, both to be held at the Losail circuit on 28 March and 4 April, will be followed up by the Portuguese MotoGP at the Algarve International circuit on 18 April.