Yankees manager Joe Girardi had limited Burnett to bullpen sessions and simulated games.
"It was nice to get out there and face some hitters," Burnett said. "It was good to get out there in live action."
Burnett's sharp outing came on the same day New York announced Rodriguez will have arthroscopic hip surgery Monday and is expected to miss six to nine weeks. The slugger will need further surgery after the season.
Detroit starter Nate Robertson gave up three hits in two innings, including a three-run homer by Angel Berroa. Robertson also had four of the 10 walks issued by Tigers pitchers.
"You give yourself no chance when you walk (that many) guys in a major league game," Tigers manager Jim Leyland said. "That's just uncalled for, in my opinion. That's uncalled for at any level, and that pretty much sums up today."
Said Robertson: "I don't want to sit here and think about all the negatives today, but I've got to be held accountable for the walks and the 0-2 pitches. I walked more today than I did all last spring."
The Yankees extended their lead to 11-0 with six runs in the fifth. Xavier Nady led off the inning with a home run off right-hander Scott Williamson.
Dontrelle Willis followed Robertson to the mound while battling a flu virus that spread through the clubhouse over the weekend. He gave up two runs in the third, then departed after pitching a scoreless fourth.
Non-roster invitee Will Rhymes hit a two-run homer off New York's Brian Bruney in the sixth.
Burnett won 10 of his last 12 decisions last season and finished with a career-best 18 victories for Toronto. His reward was an $82.5 million, five-year free-agent contract with New York.
"I'm glad we don't have to face this guy," Yankees left fielder Johnny Damon said. "He was locked in, in his first start of the spring."
Notes: Damon went 0-for-3 and struck out twice. ... Detroit's Gary Sheffield was 0-for-3, lowering his spring average to .063. ...Tigers RHP Jeremy Bonderman felt no discomfort in his shoulder during a side session.
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