Cantu homered in the third and seventh innings, his club-record fourth multihomer game of the season. He has 25 home runs, and his 105 RBI are two short of Aubrey Huff's club record.
"It would mean a lot, it's the franchise record with the bigwigs," Cantu said. "Once I get it, I'll be really proud of myself."
He's already delighted with his home run total, which leads the team.
"Actually, I am a little surprised. It was one of my goals," he said. "I was going to try to accomplish these high goals, and I'm doing it little by little. That's what matters to me right now."
Cantu, who entered 2-for-15 at Camden Yards this year, went 3-for-5. He missed Thursday night's game against the Yankees after getting hit with a pitch on the left elbow Wednesday.
"It's sore right now, believe it or not," he said.
"He took some batting practice before the game before I made out the lineup and said he was feeling good," said Tampa Bay manager Lou Piniella, who grinned and added, "[Catcher] Toby Hall said he'd like to get hit in the elbow a couple of times."
Carl Crawford homered and drove in three runs for the Devil Rays, who won at Camden Yards for the first time since July 7, 2004. Tampa Bay was 0-6 in Baltimore this season.
Kazmir (9-9) allowed one run, struck out four and walked five. The 21-year-old rookie is 6-2 in 12 starts since July 8.
"He's had a real nice first full year in the big leagues," Piniella said.
Danys Baez, the fourth Tampa Bay pitcher, got the final two outs for his 36th save.
Brian Roberts drove in the lone run for the Orioles, who finished with five hits and seven walks but stranded 11 runners.
"That's kind of been part of our problem when we aren't winning games, and even when we do," interim manager Sam Perlozzo said. "We don't seem to punch a lot of runs across."
Baltimore has scored four runs or fewer in 20 of its last 33 games.
"There's a time when the harder you try, the less you do," said Javy Lopez, who went 0-for-3. "That's what we're doing now."
The first four batters to face Rodrigo Lopez (14-10) all got hits to provide Tampa Bay with a 2-0 lead. After Julio Lugo hit
Lopez's first pitch for a double and Crawford doubled in a run on the next pitch, Cantu singled and Huff hit an RBI single.
In the bottom half, Kazmir walked three straight with two outs before striking out Alejandro Freire. The three walks were one more than Kazmir allowed in his previous two starts combined.
"It could have been a lot worse than what it was," Kazmir said. "Get the first two and feel like you're cruising, then all of a sudden I was all out of whack. It would come, then leave."
Crawford led off the third with his 14th home run, and Cantu followed with a shot to left to make it 4-0.
Baltimore got a run in the fifth when Kazmir issued two walks and Roberts hit a fly to left-center that went for a double after outfielders Crawford and Joey Gathright failed to decide who should catch it.
Lugo doubled off reliever Aaron Rakers in the seventh, stole third and scored on a sacrifice fly by Crawford before Cantu homered on the next pitch.
Crawford needs 18 hits to become the first Devil Ray to reach 200 in a season. ... Baltimore's Eric Byrnes went 0-for-3 and is in a 1-for-28 slump. ... Tampa Bay improved to 23-50 on the road, 15-15 since the All-Star break. ... Lugo made his 22nd error at shortstop, high on a team that leads the majors with 116.