The victories were Mr. Santorum’s first since the Iowa caucuses on Jan. 3 — a victory awarded only after the fact. And he used them to reassert himself as the leading insurgent challenger to Mr. Romney, though he told cheering supporters at his headquarters in St. Charles, Mo., that he was setting his sights higher than that.

“I don’t stand here to claim to be the conservative alternative to Mitt Romney,” Mr. Santorum said after thanking God for getting him through the “dog days” of the campaign and the illness of his daughter Bella. “I stand here to be the conservative alternative to Barack Obama.”

With the Colorado results still outstanding, he said the Republican voters in Missouri and Minnesota had sent a message to Mr. Romney, declaring: “Maybe in Massachusetts, they were heard particularly loud tonight.” And he called Mr. Romney an imperfect conservative messenger, saying that on health care and environmental policy, “Mitt Romney has the same positions as Barack Obama.”

But the three victories for Mr. Santorum also place a fresh burden on him as he tries to swiftly build a structure to compete with Mr. Romney’s battled-tested campaign team. His aides predicted that the evening would bring an outpouring of financial support. He also may be able to expect more help from the “super PAC” that supports him, the Red, White and Blue Fund. Its leading benefactor, the mutual fund executive Foster Friess, was standing directly behind Mr. Santorum as he gave his victory speech.

Asked by e-mail whether he would invest more heavily in the super PAC, Mr. Friess wrote back, “With him doing so well tonight, he won’t need me!”

And Mr. Santorum, whose appeal has been built on a populist message and a loyal following among conservative voters, now has the opportunity to get a fresh look by Republican voters as the nominating contest spreads across the country.