The Spaniard, who started on pole position at the Termas de Rio Hondo circuit, now has 45 points to the Italian's 41 after two races.
Italian great Valentino Rossi finished second for Yamaha with Dovizioso, winner of the Qatar season-opener, third.
"I ride like when I was young, I enjoyed it very much," said Rossi, who passed Dovizioso on the last lap, of his first podium finish as a 40-year-old and first since he was second in Germany last July.
Marquez won by more than nine seconds, making a lightning start and then pulling away to leave the rest to scrap for second.
Last year's winner Cal Crutchlow was ruled out of the reckoning after being handed a ride-through penalty for a jumped start, something the Briton felt was unwarranted.
(Writing by Alan Baldwin in London, editing by Pritha Sarkar)
