Michael took the wins in both Monday's Supersport and Superstock events.
In the day's first race, the Supersports, he led by 10 seconds over second-placed Kiwi Bruce Anstey and his brother William in third.
"Michael caught me and all I could do was sit behind him," Anstey, who is suffering from a heavy cold, admitted during the press conference after the race.
"I just got my head down," Michael, who also clocked up the race's fastest lap at 127.52mph, said.
"It was good to have Bruce behind me - it keeps your concentration right."
Both Dunlop brothers were back in action in the afternoon's four-lap Superstock event, with Michael again leading the way.
He also set himself a new lap record of 131.220mph during the final lap, on his way to winning out over second-placed Gary Johnson and John McGuinness in third.
Michael's successes on the Isle of Man circuit come after Sunday's emotional victory in the opening Superbike race.