"All dictated by pitching," Detroit manager Jim Leyland said. "Fister was tremendous. We needed to shut them down. Fister was just what the doctor ordered for us. You might have better stuff sometimes, but you can't pitch better than that. He knows exactly what he wants to do with the next pitch."
Fister (6-13) struck out five. The right-hander, acquired in a six-player trade with the Seattle Mariners on July 30, is 3-1 in five starts with the Tigers.
"My focus every time I go out there, use my fastball and my secondary (pitches) off that," Fister said.
Jackson hit a first-inning leadoff homer and made it 2-0 with a sacrifice fly in the fifth.
The Tigers took three of four from Tampa Bay and have won 16 of their last 25 road games.
"We, kind of, countered their pitching this series," Leyland said. "We got just enough to win three games, which was huge. This could have been an 0-4 trip, that's how good that pitching is. To come out of here with three wins, very pleased."
Jeremy Hellickson became the first Rays pitcher to strike out four batters in the same inning, accomplishing the feat during the third. After Jackson reached base to start the inning on a third-strike wild pitch, Hellickson then struck out Ramon Santiago, Delmon Young and Victor Martinez.
Hellickson (11-9) gave up two runs and six hits in seven innings. He had seven strikeouts and one walk.
Casey Kotchman drew a one-out walk in the ninth from Valverde and moved to third on Matt Joyce's single. The game ended when Sam Fuld lined out to right on a hit-and-run that resulted in Joyce getting doubled off at first.
"The final play of the game we caught a break," Leyland said. "If you're winning a few games, that ball's caught and you double a guy off. If you're struggling, that ball is down the line. They score the tying runs and you've got the winning run at third. That's just the way the game goes."
Fister retired his first 13 batters before Kotchman reached on a one-out infield single in the fifth. Third baseman Wilson Betemit was unable to make a backhanded grab on Kotchman's opposite-field liner.
Kotchman advanced to second when Fuld hit a two-out single, but Fister worked out of the jam by striking out Sean Rodriguez.
Kotchman singled in the seventh and went to third when Fuld doubled with two outs. Fister then retired the last batter he faced, pinch-hitter John Jaso, on a fly ball to left.
"That's the game we've played way too often this year," Tampa Bay manager Joe Maddon said. "We got great pitching from Jeremy, played really good baseball, but just not enough hitting."
Martinez doubled during the sixth and later was thrown out from right field by Joyce attempting to score on Betemit's single.
Jackson had been hitless in his previous 12 at-bats before his seventh homer this season. ... The Tigers placed first baseman Miguel Cabrera on the paternity leave list and recalled catcher Omir Santos from Triple-A Toledo. Cabrera is expected to rejoin the team on Friday. ... Santos, optioned back to the minors after the game, played in place of catcher Alex Avila, who had started the previous 18 games. ... Tampa Bay center fielder B.J. Upton (right shoulder strain) could return to the starting lineup on Friday. ... Detroit outfielder Brennan Boesch didn't play because of a sprained right thumb. He has also developed a biceps strain by compensating for the thumb and will sit out Friday's game. ... Rays right-hander James Shields (11-10) will pitch against right-hander Henderson Alvarez (0-1) in the opener of a four-game series Friday night at Toronto. ... Tigers right-hander Rick Porcello (11-8) will start Friday's game against the Minnesota Twins.