Mitt Romney drove his battered campaign to a slender victory in Michigan on Tuesday, avoiding a humiliating setback in his home state after Rick Santorum had surged into the lead.

Combined with his easy win in Arizona, Romney is roughly back to where he was before Santorum’s sweep of three contests earlier this month threw the contest into disarray.

In Michigan, Romney beat Santorum 41 to 38 percent, with Ron Paul third at 12 percent, and Newt Gingrich last with 7 percent. Romney cruised over Santorum in Arizona, 47 to 27 percent. Romney took a swipe at the “pundits and pollsters” who had counted him out. But his victory speech largely served up meat and potatoes as he promised “more jobs, less debt and smaller government … If there’s one thing we can’t afford, it’s four years of Barack Obama with nothing to answer to.” And he was still touting his résumé, saying such things as “I spent 25 years in business.”

After two weeks of dwelling on religious and social issues, Santorum delivered a concession speech heavy on economic talk. Even as he waved a pocket copy of the Constitution, he noted that The Wall Street Journal had called his plan “supply-side economics for the working man.” It was a passionate, hope-filled address, delivered without a Teleprompter, perhaps Santorum’s most uplifting of the campaign.

Had Romney lost Michigan, it would have been an extraordinary sign of weakness. He grew up there, his father ran a car company there and served as governor, and Romney easily won the state four years ago. Given his huge advantages in cash and organization, it would have been a remarkable rejection in favor of an ex-senator who got trounced in his own reelection bid six years ago.

A Michigan defeat would not have knocked Romney out of the race, but the palpable unease among party leaders would have metastasized into panic. Narrowly carrying his sort-of home state, by contrast, doesn’t do much for Mitt; he should have won in a walk.

Santorum openly appealed for Democratic votes in Michigan’s open primary, which Romney branded a “dirty trick,” although there is a long tradition of voters crossing party lines in primary states that allow it.

On the electorate front, Arizona is a bigger prize as a winner-take-all state with 29 delegates, while Michigan’s 30 delegates are allotted by proportional representation. But psychologically, and in terms of media attention, Tuesday was all about Michigan.

In light of Santorum challenging the need for everyone to go to college, it’s noteworthy that those without a college education favored Santorum in Michigan by 41 to 35 percent margin, according to CNN exit polls. Romney led among those with a college degree, 41 to 37.

A similar split on income seemed to mirror Santorum’s appeal to blue-collar voters. He led 40 to 35 percent among those earning less than $50,000, while Romney was the clear choice of those above $100,000, 47 to 35.

Not surprisingly, according to the exit polls, Santorum, with his heavy emphasis on his Catholic faith, took 62 percent of those who say religion matters a great deal to them, and 77 percent of those who named abortion as their top issue. Romney trounced Santorum, 61 to 24, among those who said the most important quality of a candidate was the ability to beat Obama, and won 55 percent of those who most valued business experience.

One statistic suggests Romney was lucky to hang on: nearly half of those who made up their minds in the last few days broke for Santorum.

Santorum openly appealed for Democratic votes in Michigan’s open primary, which Romney branded a “dirty trick,” although there is a long tradition of voters crossing party lines in primary states that allow it.

By denying Santorum a win in either state, the Romney camp slowed down what could have been a bullet train. Santorum sped to the top of the national polls after his triple triumph in Minnesota, Missouri, and Colorado. Had he followed that up by snatching Michigan, Santorum would have gotten a burst of momentum and deepened the sense that this isn’t Romney’s year.

Romney’s path to victory followed a familiar formula: outspend your opponent and rough him up in debates. At the CNN faceoff in Mesa, Romney kept Santorum on the defensive on a series of congressional votes as the Pennsylvania Republican attempted to explain why he supported bills he actually opposes.

But Santorum’s missed opportunites in the last two weeks go well beyond his fluency in Beltway-speak. He allowed himself to get sidetracked into talking about prenatal testing, contraception, and JFK’s religion speech—not to mention his complaint that President Obama “wants you to go to college … to remake you in his image.” Maybe this amounted to narrowcasting to very conservative and evangelical voters, but it can’t have been very appealing to most independents.

Santorum doesn’t have the normal political instinct for brushing aside questions that take him off message. Instead, he answers—at length—and then complains that the press doesn’t care about the rest of his platform.

Romney, for his part, seems to be surviving his gaffe-a-week performance. It’s hard to fathom why he keeps blurting out such things as that his wife drives “a couple of Cadillacs” or that he’s friends with NASCAR owners, which only deepens his out-of-touch-rich-guy persona. And while his speech at a mostly empty Ford Field was a logistical disaster, it’s also true that the press has been ignoring his economic proposals—such as returning the food-stamp program to the states—in favor of a focus on optics.

But even after saying he likes firing people and doesn’t care about the very poor, Romney somehow keeps winning primaries. Either his competition is amazingly weak or he is one resilient politician—that, or a very lucky one.