Gardner, who finished second at the season-opening Qatar GP last month, crossed the line in the same position at the Doha GP.
The Red Bull KTM Ajo rider was beaten to the chequered flag on Sunday by just 0.190 seconds in a thrilling battle with Sam Lowes (Elf Marc VDS Racing Team).
Lowes, who also won the first Moto2™ race of 2021, leads the World Championship standings on 50 points, closely followed by Gardner on 40.
“I’m very happy with the race,” Gardner said.
“From the start I saw that the rider at the front was pushing very hard, and with each lap we were going faster because his pace was incredible.
“At the end of the contest, I thought I had to give it a go, and I gave it everything.
“I almost managed to pass him, but I didn’t want to make mistakes just because I wanted to claim five more points.
“I’m satisfied and surprised to see the good pace we had. We achieved points that are positive for the World Championship.”
Gardner’s teammate Raul Fernandez (27 points) is third in the standings after he sensationally completed the podium at the Doha GP in just his second appearance in the intermediate class.
Team manager Aki Ajo said it was an excellent result for his Red Bull KTM Ajo squad in Qatar, where pre-season testing and the first two races of the season were held.
“It’s amazing for both riders to have got on the podium,” he said.
“We are happy for Remy, who earned 20 points which are important in a season as long as this one.
“We are pleased to see his progress, especially this weekend. He improved a lot and prepared well for the contest.”
Moto2™ returns to action in two weeks’ time, at the Portuguese GP on 16-18 April.