The Andretti Autosport driver led 50 of the 75 laps completed before the race hit its two-hour maximum duration.
He headed Simon Pagenaud, who scored his best result since switching from Team Penske to Meyer Shank Racing over the off-season, while polesitter Will Power (Penske) took the lead of the championship by finishing third.
With a wet race declared on the damp track, Power lost out at the start to Alex Palou (Chip Ganassi Racing) and his team-mate Josef Newgarden. Behind them, Pato O’Ward moved up to fourth, but had soon made his way into the lead while Arrow McLaren SP team-mate Felix Rosenqvist also made short work of Palou to run second.
In his first of two decisive strategic gambles, Herta pitted for the red-sidewalled soft compound Firestone slick tyres on lap three together with Dale Coyne Racing's Takuma Sato.
Although the leaders soon followed his example, Herta’s pace was so strong on slicks that he made huge ground and was quickly onto the tail of O'Ward - surviving a huge opposite-lock slide through Turn 8 to pass the Mexican for the lead.
Following a caution required when Palou spun exiting Turn 4 and stalled, requiring him to be restarted by the AMR Safety Team and resume a lap down, Herta continued to lead O'Ward and Rosenqvist with Power fourth.
Newgarden had passed a fuel-saving Conor Daly (Ed Carpenter Racing) for fifth, but his race was ended in contact with Alexander Rossi (Andretti) and Jack Harvey (RLL) after the two-time champion lost momentum being passed by Sato.
Sato claimed fourth from Power at the restart, but the race was immediately halted again when ECR driver Rinus VeeKay rejoined from a grassy moment and left Andretti's Devlin DeFrancesco with nowhere to go.
Following the third caution, Power continued to lose positions, falling behind Harvey and Rossi - who had both continued after the Newgarden incident.
Rosenqvist jumped O'Ward at the next pit cycle by staying out a lap longer than his team-mate, and two longer than Herta. The Swede emerged from the pitlane alongside Herta, but had to give best and fall in behind.
Rain arrived during the race's fourth caution, when Dalton Kellett spun his Foyt car across the grass at Turn 6, but the leaders remained on slicks.
As an off-strategy Marcus Ericsson (Ganassi) and Kyle Kirkwood (Foyt) led the field to the green, O'Ward aggressively passed Rosenqvist but then rotated himself trying to pass Herta - and was collected by Rosenqvist, while Sato was forced onto the grass in avoidance.
O’Ward got going again unassisted but Rosenqvist stalled, requiring a fifth caution during which Kirkwood followed Rossi and Palou in taking on wets. Their gamble would backfire however, prompting a return to the pits for another set of slicks.
Ericsson led Scott Dixon to the next restart - the Kiwi having gone a lap down when he ran out of fuel in the opening stint - with Herta followed by Scott McLaughlin (Penske), Harvey and Romain Grosjean (Andretti).
But a struggling Ericsson soon tumbled back down the order after being passed by Dixon and Herta, who again put Dixon a lap down shortly afterwards. McLaughlin, Harvey, Grosjean, Pagenaud, Power and the recovering O’Ward gave chase.
Grosjean's charge to the front was disrupted when he was run out wide by Harvey at Turn 7 and spun, which allowed Pagenaud to pass the pair of them for third. Power tried to pass Harvey too, but was elbowed sideways by the RLL car and lost a spot to O’Ward - who took fourth from Harvey one lap later.
O’Ward continued his progress by taking Pagenaud for third on lap 55, just before the sixth caution of the day arrived for Ganassi driver Jimmie Johnson stalling after a spin.
Following the next round of stops on lap 59, the leaders elected to remain on slicks despite the rain returning. McLaughlin rejoined ahead of Herta, with O’Ward third ahead of Pagenaud, Harvey, Power, Callum Ilott (Juncos-Holinger) and Grosjean.
But when VeeKay spun and stalled under caution, causing an extension to the yellow period, several of the leaders came back in to change to wets. McLaughlin, O’Ward and Grosjean remained out on slicks and were due to lead to the restart - only for McLaughlin to spin and drop to sixth.
O’Ward's slick tyre gamble put him in the lead, but Herta on wets was soon past him at Turn 1. As rain continued, McLaughlin spun at Turn 3 and stalled, while O'Ward also spun at Turn 1 - putting Pagenaud into second and Power into third. O’Ward then elected to pit on the restart.
Herta, Pagenaud and Power escaped at the restart with seven minutes to go, while Daly staved off Juan Pablo Montoya (Arrow McLaren SP) into Turn 1 for fourth. Neither could repel the charging Ericsson however, the Swede grabbing fourth from Daly as his compatriot Rosenqvist demoted his team-mate to claim sixth.
When Montoya struck a wall, the yellow came out one final time to neutralise the action for good.
Behind Rosenqvist, Sato took seventh, while Ilott finished eighth but was rammed by RLL's Christian Lundgaard as they passed the checkered flag.
