NOVI, Mich. — Overcoming his own stumbles and what he called one opponent’s “dirty trick” campaign, Mitt Romney swept both the Arizona and Michigan primaries on Tuesday, once again taking control of the Republican presidential race and earning valuable momentum as the field prepares for Super Tuesday next week.

In winning Michigan, Mr. Romney claimed victory in the state where he was born and where his father served as governor — and avoided what would have been an embarrassing loss.

And in both Arizona and Michigan, he improved on his showing from 2008, breaking what had been a trend of shedding support from his prior run.

Shortly after the networks projected Mr. Romney’s victory, his supporters broke into cheers at his victory party, and Martha and the Vandellas’ Motown hit “Dancing in the Streets” began playing.