Across six innings in a 103-pitch outing, Glasnow (8-5) yielded one run on three hits and one walk.
The 6-foot-8 right-hander rounded out his start by fanning six consecutive batters in the fifth and sixth innings. Glasnow's only previous 14-K game came against the Texas Rangers on April 12, 2021.
Brandon Lowe and Isaac Paredes both homered and Harold Ramirez doubled home a run as Tampa Bay (85-55) improved to 9-2 this season against the Red Sox (72-68).
Pete Fairbanks struck out two in a scoreless ninth for his 20th save in 22 chances.
The Rays added to their sterling home record against Boston, beating their division rival for the 15th time in the past 16 matchups in the dome.
For the Red Sox, Connor Wong had an RBI triple, but the visitors produced only five hits and fanned 17 times, including seven straight midgame.
Injured on Sunday, Boston outfielder Alex Verdugo (left hamstring tightness) did not play and missed the entire series.
In the third inning, Boston went up 1-0 with no outs on Wong's triple, a high shot into the right field corner that plated Enmanuel Valdez, who had singled.
Glasnow, who had recorded five strikeouts in the first two frames, left Wong stranded at third after a diving stop by shortstop Osleivis Basabe was surrounded by Wilyer Abreu and Justin Turner both looking at third strikes.
Lowe, the hero on Tuesday with a walk-off homer in a 8-6, 11-inning win, went deep on a four-seam fastball from Nick Pivetta (9-8) with two outs in the bottom of the first on Wednesday.
He ripped his game-tying 19th long ball out to right-center at 109.2 mph at 416 feet, giving him 18 homers in 53 career games against Boston.
Paredes took Pivetta deep with two outs in the fourth, hammering a 3-2 four-seamer for his 28th homer and 87th RBI for a 2-1 lead.
The Rays made Pivetta pay for wildness in the fifth. After two walks, Ramirez's two-out double off the center field wall sent home Yandy Diaz and chased Pivetta after 4 2/3 innings. The right-hander yielded three runs on seven hits and two walks while striking out five.
—Field Level Media