DETROIT -- A healthy Joe Kelly on the mound in the bottom of the eighth inning on Tuesday night was definitely a welcomed sign for the White Sox, particularly after they learned they’d lost All-Star closer Liam Hendriks to the injured list just a few hours prior to first pitch.

What Kelly did when he took the ball was even better.

Tuesday's 5-1 victory over Detroit guaranteed a series win for Chicago, which will go for a three-game sweep during a Wednesday matinee. Perhaps even more importantly, it brought Kelly’s return to action, a positive sight for a beleaguered White Sox bullpen that is slowly but surely inching toward replenishing its resources.

“We have no fear to bring him into a situation,” manager Tony La Russa said. “Those guys in the middle [of the Tigers’ lineup]; if they were hitting in the ninth, Kelly would’ve pitched the ninth.

“It was great to see him out there. He’s really got a lot of weapons.”

Kelly had been shelved with a left hamstring strain since May 26, but he pitched so well in a recent simulated game that the White Sox weren’t even compelled to send him on a rehab assignment before he rejoined the club. Kelly wasted no time in showing them they’d made the right call, dispatching the heart of Detroit’s lineup in order.

Kelly showed no signs of rust from his three-plus weeks away, working with a comfortable lead and flashing a cutter and sinker that left Tigers batters scratching their heads during the perfect frame. He drew four swings on his 11 pitches and three of them missed, as he fanned Javier Báez looking and Robbie Grossman swinging.

All three misses came on Kelly’s high-80s cutter that played smartly off a high-90s sinker that coaxed Austin Meadows into a harmless groundout for the remaining out of the eighth.

Long before Kelly did his thing, though, the stage belonged to Dylan Cease. The right-hander needed 108 pitches to get through five innings, but he limited the damage to a single unearned run and fanned eight.

Things were a bit sticky for Cease in the early going as he worked to find a groove, loading the bases with one out during a 29-pitch first inning to prompt a mound visit. He tried to redeem himself with a pickoff move to second base, but the throw bounced out of shortstop Danny Mendick’s glove and dribbled into the outfield, allowing Victor Reyes to score easily from third.

“I ran into a little bit of trouble in that first inning, but I was able to compete and get through five,” Cease said. “I would have liked to have gone deeper and just help the ‘pen a little bit more, but it was good for the most part.”

It began to come together for 26-year-old soon after, and he allowed just two singles over the next two innings combined before sitting down the side in order in the fourth.

“If he’d have struggled in the fourth, he’d have never pitched the fifth [because of his pitch count],” La Russa said, “but the fourth was about as good as he’d looked, so he went out for the fifth."

Detroit didn’t score after the first inning on any Chicago pitcher, including Jimmy Lambert, who worked a crisp sixth and seventh frames, and Reynaldo López, who slammed the door in the ninth.

“[Lambert has] really been impressive,” La Russa said. “He’s really got a good array of stuff, and he commands three or four pitches just like a starter.”

With the win, Cease moved to 10-0 with a 1.91 ERA and 75 strikeouts in 11 career starts against Detroit. Whatever the reason for the amount of success he’s had against his American League Central foe, Cease said he’s not complaining.

“It’s obviously great,” said Cease, who drew 15 swings and misses on the night, more than twice the amount of his Detroit counterpart Drew Hutchison. “I try not to give it too much stock because I don’t want to jinx myself. It’s something cool and something special, for sure, but there’s still more work to be done, so it’s not something I’m going to coast on, by any means.”