Having fended off threats from Palou and Grosjean, the Penske driver took the team's third consecutive win after a crash-strewn race.
It marked Newgarden's 22nd career victory, equaling Tony Bettenhausen and Emerson Fittipaldi in the record books.
Former Formula 1 driver Grosjean took his second series podium, having been denied pole for Sunday's race after a crash in qualifying, while defending champion Palou took third place for Chip Ganassi Racing.
Having started in second, Newgarden was left trailing by Andretti Autosport driver Herta's perfect start and was forced to fend off Palou in the opening stages.
The trio ran out front for much of the distance, with Palou leading from Newgarden and Herta after pitting early.
But a crash from Herta at Turn 9 on an in-lap, locking up over a bump and understeering into the outside wall, coupled with a cleverly timed pitstop put Newgarden into the lead with 19 laps remaining.
At the restart, Newgarden held off Palou, but behind them, Palou's team-mate Marcus Ericsson lost the rear of his car exiting Turn 4, tagging the wall with his left rear.
Grosjean and Will Power (Team Penske) ducked through, but as Ericsson pulled over to the right to park it on the inside of Turn 5, Scott Dixon ran into the back of him. This allowed Arrow McLaren SP's Pato O’Ward to slip past the six-time champion, although Dixon escaped without damage.
Grosjean, on alternates, then attempted to pass Palou for second into Turn 1 on lap 69. Although that attempt failed, the Andretti driver repeated the effort on the following tour, and this time was further ahead into the brake zone, so carved across and claim second.
Grosjean immediately started applying the pressure on leader Newgarden, who was looking scrappy in defence, but the Frenchman ran out of push-to-pass boost.
However, he would get another chance at tackling Newgarden (who had 4s P2P left) as Jimmie Johnson’s torrid weekend finished slightly early after sliding his Chip Ganassi car into the Turn 8 tyres, and being collected by David Malukas of Dale Coyne Racing.
The restart with four laps to go saw Grosjean try to make the pass into Turn 1, but Newgarden’s defence on the inside line was enough to rebuff him. A lap later, Newgarden used his last spurt of P2P to launch off the hairpin, and he was effectively safe for another lap.
He also remained ahead without an apparent threat from Grosjean on the penultimate lap, before the yellow had to come out once more when Sato - who had earlier clashed with Simon Pagenaud at the Fountain - slid into the tyres in Turn 8 and couldn’t restart.
Palou held on to finish third, with Power in fourth ahead of O'Ward and Dixon.
