His next task, say political analysts, will be to harness that momentum into more wins in order to seriously hobble Donald Trump’s front-runner status and make himself the best establishment alternative to Trump or Sen. Ted Cruz, R-Texas.

>> PHOTOS: Notable supporters of 2016 presidential candidates

“I think he’s hoping as the last man standing he can be a contender at the convention,” said John Feehery, a Kasich supporter and onetime adviser to former House Speaker Dennis Hastert, R-Ill. Tuesday’s victory, he said, “has to be the start of a bigger process by which it becomes clear Trump is seriously weakened.”

Trump, however, had a nice night Tuesday. Although he lost big to Kasich in Ohio, he won two other big states — Florida and Illinois — and also won North Carolina.

Kasich, meanwhile, finished a distant third in Illinois, Missouri and North Carolina, and came in fourth in Florida, which he all but abandoned as he focused on campaigning in his home state.

Of the remaining GOP candidates in the race, Kasich is far behind in delegates: He had 63 before winning Ohio, while Trump had 463, Cruz had 370 and Rubio had 163 before Tuesday’s ballots were counted. Trump by far had the biggest haul of the night, helped by the 99 delegates he won in Florida.

>> Read more trending stories

There are no longer enough delegates available for Kasich to win the nomination on the first ballot.

“The law of mathematics is a stubborn thing,” said Barry Bennett, an unpaid adviser to Trump. “There are not enough delegates for (Kasich) to get the nomination. Their only option is to try and stay alive financially until the convention. I don’t know what you do at the convention with 150 delegates.”

But with Sen. Marco Rubio’s exit from the race after his loss in Florida, Kasich has the so-called establishment candidate lane to himself.

“What it tells us about Kasich is he can win his home state while Marco Rubio couldn’t,” said Stuart Rothenberg, editor of the non-partisan Rothenberg Political Report. “Now the question is to what extent can Kasich capitalize on that and establish himself as the candidate of the GOP establishment.”

Though Trump had focused much of his Twitter rage on Kasich in the days leading up to the election, Rothenberg said Kasich has been largely “untouched” by the other candidates, who have not attacked him with much vigor. “He’ll start taking some heat,” Rothenberg said.

Jennifer Duffy of the nonpartisan Cook Political Report said while Kasich winning enough delegates in the remaining contests is “off the table,” Tuesday’s win “keeps him out there campaigning.”

“After tonight, if he can pick up more delegates, it gives him yet more influence if the convention is contested,” she said.

He’ll have opportunities in Wisconsin, which votes April 5; Pennsylvania, which votes April 26; and Indiana, which votes May 3. But many of the states ahead on the calendar are winner-take-all, meaning Kasich can’t settle for coming in second.

Trump is still the odds-on favorite for the nomination.

“The biggest problem the Republicans have is it’s going to be awfully hard to take on Donald Trump at a convention unless he is seriously weakened on the path there,” said Feehery.