Santorum, a former U.S. senator from Pennsylvania, leads among likely Republican voters in the Bayou State with 37 percent of the vote, a March 19 Magellan Strategies BR poll indicated.
Romney, a former Massachusetts governor, came in second place with 24 percent, the poll found.
Former U.S. House Speaker Newt Gingrich of Georgia had 21 percent and U.S. Rep. Ron Paul of Texas had 3 percent, the poll indicated.
Gingrich's candidacy "clearly hurts Santorum's position in Louisiana," Magellan Strategies said. If Santorum faced only Romney, he would win Louisiana 55 percent to 34 percent, the poll found.
The survey of 2,018 likely Republican primary voters in Louisiana has a 2.18 percent margin of error.
Romney won the industrial Midwest state of Illinois Tuesday night with 46.7 percent of the vote, compared with Santorum's 35 percent, with 99 percent of the vote counted.
Paul came in third with 9.3 percent and Gingrich had 8 percent. Other candidates took 1 percent of the vote.
Romney was poised to collect about three times as many Illinois delegates as Santorum, The New York Times reported.
Addressing supporters in a hotel ballroom in the Chicago suburb of Schaumburg, Romney congratulated his rivals and then turned his focus to President Barack Obama.
He belittled Obama's experience as a constitutional law professor at the University of Chicago and as a community organizer on Chicago's South Side, saying Obama's background before running for office gave him little understanding of how to shepherd the economy.
"You can't learn that teaching constitutional law. You can't learn that as a community organizer,'' Romney said.
"It's time to say this word -- enough. We've had enough," he said.
"I'm running for president because I have the experience and the vision to get us out of this mess," he said.
Santorum told supporters Tuesday night Romney's background as an investor and management consultant is not what America needs.
"We don't need a manager," he told an overflow crowd in Gettysburg in his home state of Pennsylvania. "We need someone who is going to pull up government by the roots and throw it out and do something to liberate the private sector in America."
Gingrich, who made little effort to campaign in the Illinois primary, did not give a speech Tuesday night, but in a statement offered no indication he would bow to pressure to drop out of the race, despite a poor showing and winning only two primaries so far.
"To defeat Barack Obama, Republicans can't nominate a candidate who relies on outspending his opponents" by large margins, he said. "Instead, we need a nominee who offers powerful solutions."
Paul, who also made little effort to campaign in Illinois, made no appearance and did not immediately release a statement.