Rondon struck out the side and around a two-out walk in the fifth inning. He was the likely closer when camp opened last month, then struggled early in spring training.
''He looked pretty good today,'' Leyland said. ''He looked pretty good his last outing. Didn't look too good a couple outings. We're just watching and looking. He has a lot of physical ability. A lot.''
Hill, likely to start the season at Triple-A, struck out three and walked one. Rondon, Jose Alvarez and Luke Putkonen finished the four-hitter as the Cardinals were shut out for the third time in six games.
Rondon, a 25-year-old right-hander, had a 1.53 ERA and 29 saves last year at three minor league levels, While the top candidate to take over from Jose Valverde, who became a free agent, Rondon allowed three runs over consecutive outings on March 1 and 3. Against the Cardinals, he struck out prospect Oscar Taveras, Ty Wigginton and Ronny Cedeno around Tony Cruz's walk in the fifth.
''You guys need to get off the closers kick,'' Leyland told reporters. ''It's going to go to the wire because I have no idea. I wish I could tell you but I can't. There's no sense talking about it. Just watch Rondon, I'll give you my opinion of what I thought of the performance, but there's no sense in, `Well are we getting closer to the closers role?'''
Hill, who played for Canada in the World Baseball Classic, got the start in part because the Tigers didn't want to make Justin Verlander take the three-hour bus trip across the state.
''I thought he did very well today,'' Leyland said. ''He sunk the ball. He wasn't overpowering but he did what he supposed to do, sunk the ball and kept the ball on the ground, mix his pitches pretty good, attack the strike zone pretty good. I thought he had a good outing. I was impressed.''
Left-hander Jaime Garcia gave up all three runs and six hits in five innings for the Cardinals. He has a 3.00 ERA in four exhibition starts.
''I thought it was a good outing,'' Cardinals manager Mike Matheny said. ''I don't think his health is a question. I was hoping we cleared that up and I think he has by the way he's pitched but he'll just have to keep going out there and hopefully answering those questions by how he pitches. He's throwing the ball well. It's what we expect from him.
Go out there and be the guy that he can be.''
Matt Carpenter had one of the Cardinals' hits and is hitting .410 (16 for 39).
NOTES: Tigers OF Avisail Garcia left the game with a bruised right heel after hitting first base awkwardly while trying to beat out an infield single. He is day to day. ... RHP Anibal Sanchez will start on a back field Sunday in Lakeland. He's returned to the Tigers following his stint with Venezuela in the WBC. ... Cardinals 3B David Freese was not in the lineup for a second straight day due to back tightness. ... Cardinals RHP Mitchell Boggs returned to camp from the WBC after the U.S. was eliminated Friday.
Link to box score: Detroit 3 at St. Louis 0