The former Massachusetts governor got 43 percent of Wisconsin's vote, 49 percent of Maryland's and 70 percent of Washington's, unofficial results monitored by United Press International indicated.
Rick Santorum, a former U.S. senator from Pennsylvania, came in second with 38 percent in Wisconsin and 29 percent in Maryland. He was not on the Washington ballot.
Former U.S. House Speaker Newt Gingrich from Georgia took 6 percent in Wisconsin and 11 percent in Maryland and Washington. U.S. Rep. Ron Paul of Texas tallied 12 percent in Wisconsin, 10 percent in Maryland and 12 percent in Washington.
"The dreamers can dream a little bigger, the help-wanted signs can be dusted off, and we can start again," Romney said in a victory speech in downtown Milwaukee. "And this time we'll get it right."
Romney didn't mention his Republican rivals, training his fire exclusively on Obama.
"This campaign is going to deal with many complicated issues, but there is a basic choice we're going to face," he said. "The president has pledged to transform America and he has spent the last four years building a government-centered society. I will spend the next four years rebuilding the foundation of an opportunity society led by free people and free enterprise."
Santorum turned his attention to his home state of Pennsylvania, which he said Sunday he would have to win to remain relevant.
That primary -- along with those in Connecticut, Delaware, New York and Rhode Island -- is to be held April 24. A total of 231 delegates are at stake, with the most, 95, in New York, followed by Pennsylvania, with 72.
Santorum declared in a defiant speech in Mars, Pa., that the race was at its halfway point, and said he wasn't about to quit now.
"Pennsylvania and half the other people in this country have yet to be heard," Santorum told supporters.
"After winning this state, the field looks a little different in May," he said.
He predicted he would win the Texas primary, with 155 delegates at stake, May 29.
A fresh poll from Quinnipiac University shows Santorum leading Romney in Pennsylvania 41 percent to 35 percent among likely voters. Paul came in at 10 percent, followed by Gingrich at 7 percent.
The March 27-April 1 phone survey of 647 likely Republican primary voters had a probable margin of error of 3.9 percentage points.
With Tuesday's triple victory, Romney won most of the 100 delegates in play.
Romney entered the day Tuesday with an estimated 568 to 571 delegates to Santorum's 272 to 274. Gingrich had 135 and Paul had 51.
A candidate needs 1,144 delegates to clinch the nomination. Nineteen Republican contests remain before the Republican National Convention in August.
Obama mentioned Romney by name for the first time Tuesday in a major address dedicated to the budget championed by Romney supporter Rep. Paul Ryan, R-Wis.
Obama called the budget a "radical vision" and "thinly veiled social Darwinism" that amounted to "a prescription for decline" in the country.
"[Romney] said that he's 'very supportive' of this new budget," Obama told an American Society of News Editors luncheon in Washington. "And he even called it 'marvelous' -- which is a word you don't often hear when it comes to describing a budget. It's a word you don't often hear generally."
His comments about Romney's budget characterization drew laughter among the audience, which -- because it was made up of professional journalists -- was otherwise not very demonstrative.
The Romney campaign was expected to announce Wednesday morning it would begin raising funds for the general election, including through a joint fundraising operation with the Republican National Committee.