Gibson mixed in his slider and placed new emphasis on his changeup in striking out Rays slugger Evan Longoria three times and leadoff man John Jaso twice.
"I think it's a pitch just to throw into the arsenal," Gibson said of his changeup. "I think it's just going to make my fastball better, which is the one thing I was looking for."
The right-hander had just 107 strikeouts in 179 1-3 innings last season, his first full year in the majors. He has 17 Ks in 19 2-3 innings this spring.
Rene Rivera, the second batter of the game, homered, but the only other hit off Gibson was a two-out single by Desmond Jennings in the fourth. Gibson retired seven of his final eight batters, issuing a full-count walk to No. 9 hitter Tim Beckham in that span.
"We need a higher foul pole," Twins manager Paul Molitor said.
Twins switch-hitter Kennys Vargas hit a long home run in the sixth inning, batting from the right side, that nearly cleared the boardwalk beyond the left field berm. It was Vargas' team-high fourth homer of the spring.
Rays: RHP Matt Andriese struck out six in his five shutout innings, including two of leadoff man Brian Dozier. Andreise, who has emerged as a surprise frontrunner for the fourth spot in the rotation, has a 1.10 ERA in 16 1-3 spring innings.
"I thought Matt Andriese was outstanding," Rays manager Kevin Cash said. "His changeup was really good."
Twins: Gibson has struck out seven or more just three times in 41 big league starts. Two of those games came in his final 12 starts of 2014, including a career-high eight strikeouts on Sept. 23 against the Arizona Diamondbacks.
Rays: Rivera, who had missed several days with left calf tightness, was able to catch five innings without issue. He also grounded out and struck out in addition to his second homer of the spring.
Twins: C Josmil Pinto (head injury) was cleared to resume baseball activities Wednesday. He ran, threw and took some swings in the batting cage, but he has not done any catching work since being hit by three follow-throughs of swings by Adam Jones on Saturday against Baltimore. The Twins are hopeful Pinto, still competing for a backup spot, could return to action on the minor league side in the next few days. ... LHP Brian Duensing (bruised left quadriceps) will be out a few days after taking a comebacker off the leg by Toronto's Devin Travis. "He's all right," Twins general manager Terry Ryan said, "but that was a pretty good bolt. I'm glad it didn't hit him on the knee."
Rays: RHP Kevin Jepsen will start Thursday at home against the New York Yankees.
Twins: LHP Tommy Milone, the presumed frontrunner in a three-way competition for the final rotation spot, will start Thursday at the Boston Red Sox.