Mr. Santorum was expected to do well in the strongly conservative state, where rivals Mitt Romney and Newt Gingrich did not campaign.
He needed to do well in Kansas to keep alive his hopes of winning the ticket.
Meanwhile, Mr. Romney claimed victory in Wyoming, Guam, the Northern Mariana Islands and the US Virgin Islands.
Mr. Santorum was under pressure to catch up on Mr. Romney since trailing him on Super Tuesday.
Mr. Romney won the lion’s share of the 10 contests on Tuesday, taking the crucial swing state of Ohio by a narrow margin and racking up five other victories.
Mr. Gingrich won Georgia on Tuesday but did not achieve the sweep of Southern states that he had hoped for.
The state of Wyoming completed its caucuses on Saturday but there is no formal process for translating the results into delegates for the Republican’s national convention.
Before Saturday’s contests, Mr. Romney had 441 delegates committed to his nomination while Mr. Santorum had 183 out of the 1,144 needed. Mr. Gingrich trailed with 107 and Ron Paul, who also campaigned in Kansas, had 46.
A later tally by the Associated Press taking into account the latest results left Mr. Romney with 453 delegates – more than all his rivals combined. Mr. Santorum had 217, while Mr. Gingrich still had 107 and Mr. Paul had 47.
Final returns in Kansas showed Mr. Santorum with 51% support, Mr. Romney with 21%, Mr. Gingrich with 14% and Mr. Paul with 13%.
The Republican governor of Kansas, Sam Brownback, had attended rallies both for Mr. Paul and Mr. Santorum on Friday, but did not endorse either.
“Since Romney and Gingrich have decided not to campaign in Kansas, we feel pretty confident that we’re going to do well,” Mr. Santorum told BBC reporters.
Speaking at a rally in Wichita, he sought to liken Mr Romney to President Barack Obama while comparing himself to the late Republican president, Ronald Reagan.
“We already have one president who doesn’t tell the truth to the American people – we don’t need another,” Mr Santorum said to cheers from hundreds of supporters in an aircraft hangar.
“Governor Romney reinvents himself for whatever the political occasion calls for.”
Mr Romney has been campaigning in Alabama, which holds its contest on Tuesday along with Mississippi.
“Washington insider Rick Santorum is lashing out at Mitt Romney because he can’t accept the fact that it’s nearly impossible for him to win the number of delegates needed to secure the Republican nomination,” said Mr. Romney’s spokeswoman, Andrea Saul.