Gingrich said his campaign will spend the time leading to the party convention "relentlessly taking the fight to President Obama."
Illinois fell into Romney's column far more easily than Michigan or Ohio had.
The night's vote count was plagued by ballot difficulties. Rupert Borgsmiller, executive director, of the Illinois State Board of Elections, said in late afternoon that 25 counties and the city of Aurora were affected by the ballot problem. He didn't know how many ballots were affected but said "clearly you can say more than hundreds."
Romney and Santorum campaigned energetically across the state, and not always in respectful tones.
"Senator Santorum has the same economic lightweight background the president has," Romney said at one point. "We're not going to replace an economic lightweight with another economic lightweight."
Santorum had a tart reply. "If Mitt Romney's an economic heavyweight, we're in trouble."
Anticipating a primary defeat, Santorum's campaign argued that the race for delegates is closer than it appears.
Santorum contends the Republican National Committee at the convention will force Florida and Arizona to allocate their delegates on a proportional basis instead of winner-take-all as the state GOP decided. Romney won both states.
On Tuesday, about four in 10 voters interviewed as they left their polling places said they were evangelical or born again. That's about half the percentage in last week's primary states of Alabama and Mississippi, where Santorum won narrowly. Despite an unusually lengthy race for the nomination, less than a third of those voting said in the polling-place survey they hoped the primary season would come to a quick end even if that meant their candidate might lose the nomination.
The findings came from preliminary results from the survey of 1,555 Illinois Republican voters, and had a margin of error of plus or minus 4 percentage points. The exit poll was conducted for The Associated Press and the television networks by Edison Research at 35 randomly selected polling places around the state.
As Illinois Republicans voted on Tuesday, Romney raised more than $1.3 million at a luncheon in Chicago.
Santorum, the former Pennsylvania senator, has been seeking to make up in broadcast interviews what he has lacked in advertising money.
On Monday, his campaign began before sun-up and ended well after dark, including four appearances at rallies around the state as well as an extraordinary 19 radio and television interviews. He accused Romney anew of putting his signature on a Massachusetts health insurance law that is similar to the one Obama pushed through Congress.
Romney cut short his planned time in Puerto Rico, site of a primary last weekend, to maximize his time in Illinois. He has eked out victories in other big industrial states over the past few weeks, beginning in Michigan on Feb. 28 and Ohio on March 6. Defeat in any would be likely to trigger fresh anxiety within the party about his ability to wrap up the nomination.
Illinois was the 28th state to hold a primary or caucus in the selection of delegates to the nominating convention, about halfway through the calendar of a Republican campaign that has remained competitive longer than most.
A change in party rules to reduce the number of winner-take-all primaries has accounted for the duration of the race. But so has Romney's difficulty in securing the support of the most conservative of the GOP political base. Santorum and Gingrich have struggled to emerge as the front-runner's sole challenger from the right.
Whatever the reasons, the race appeared unlikely to end soon, with Santorum and even Gingrich vowing to campaign into the convention.
Romney triumphed after benefitting from a crushing advantage in the television advertising wars, and as his chief rival struggled to overcome self-imposed political wounds in the marathon race to pick an opponent to Democratic President Barack Obama.