The Northern Irishman, who dominated Race 1 on Saturday to win by nearly four seconds, raced through the field and passed Michael Ruben Rinaldi in second to set up an epic battle with Chaz Davies over nine laps, before clinching the victory.
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Meanwhile, Marco Melandri and Michael van der Mark crashed on lap 10 and neither rider could return to the race.
Tom Sykes - Rea's team-mate - finished third, with Xavi Fores in fourth.
The victory further extends Rea's lead in the championship to 47 points and means he equals Fogarty's career-wins record of 59 and sets a new record of doubles at the same circuit, with 17.
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