Lorenzo has five podium finishes in six starts at Indianapolis, the most of any rider.
Valentino Rossi, the inaugural Red Bull Indianapolis GP winner in 2008, passed Cal Crutchlow for fourth place in the final turn of the race.
After leading 22 laps of the Moto2 race and controlling the action, Takaaki Nakagami gave up the lead to Esteve Rabat as the driver from Spain made a daring pass and held on for the win.
“I push at the end and take pass and push as hard as I can,” Rabat said. “At the end we make very good job and finish.”
The win marks Rabat’s second career Moto2 victory and second of the season. With the win, Rabat became the fourth consecutive Spanish rider to win the Intermediate class of the MotoGP World Championship.
The Moto3 race was a back and forth affair for all 24 laps and featured 12 lead changes. Estrella Galicia teammates Alex Rins and Alex Marquez battled it out throughout the race, culminating with an exciting finish.
On Lap 22, Marquez passed Rins in Turn 1 for the lead and on very next, and final, lap Rins returned the favor in the same corner, passing Marquez and taking the win by .177 seconds.
The victory marked Rins’ third career Moto3 win and third this season. It was also his second consecutive triumph as he also won the German Grand Prix last month.