If last week’s major-league debut felt tense, Michael Kopech faced a few more nail-biting moments — including a couple of bases-loaded situations — during his second start Sunday against the Tigers.

The White Sox pitching phenom gave up his first earned run. And he picked up his first major-league win — a 7-2 Sox victory at Comerica Park.

Kopech talked Saturday about improving his command, and, as evidenced Sunday, when it’s on, it’s on. He threw 86 pitches — 61 for strikes, in six innings.

But when he was off, he was way off, nailing a couple of batters in the back.

All in all, the Sox have to like how the young pitcher worked his way out of trouble. He gave up seven hits but limited the damage to Victor Martinez’s RBI-double in the sixth.

The Tigers loaded the bases after that, but Kopech kept feeding Ronny Rodriguez fastballs on the outer edge — three went for balls — and got him to ground into an inning-ending double play to short.

Kopech also had a bit of a scary moment — at least for Sox fans — when Mikie Mahtook’s single deflected off his leg in the second inning. Kopech appeared to shake it off, but manager Rick Renteria and trainer Herm Schneider came out to check him out. Kopech took a practice pitch and kept going.

He challenged righties and lefties alike inside the zone and got Ronny Rodriguez to pop out on a 1-1 fastball to end the inning.

He later nailed two batters in the back — the second one loading the bases.

Avisail Garcia got the scoring going in the third inning with an RBI-double off Jordan Zimmermann, who struck out five Sox but gave up five runs on eight hits.

Daniel Palka followed Garcia with a 407-foot blast to right field, his 19th homer of the season. He came into the game hitting .378 in his career against the Tigers.

Adam Engel scored on Tim Anderson’s sacrifice in the seventh when Mahtook’s throw from left bounced over the head of catcher James McCann for an error.

Moncada drove in a run for the third straight game with an RBI triple in the sixth.

Hector Santiago got the call in the ninth with the Sox leading 7-1 and served up a leadoff home run to Ronny Rodriguez. After Santiago, who had a 1.37 ERA over his previous 11 outings, loaded the bases, Jace Fry came in and escaped the jam.

The Tigers held a pregame ceremony to retire Alan Trammell’s No. 3.

plthompson@chicagotribune.com

Twitter @_phil_thompson