Meeks scored 16 of his 27 points in the second half and Stevenson added 16 points and 12 rebounds to lead Kentucky to a 61-51 comeback victory over Alabama on Saturday that only came after a halftime scare.
The Wildcats (16-4, 5-0 Southeastern Conference) overcame a six-point halftime deficit and the collapse of Harris outside the locker room before the second half started.
Harris was taken to a nearby hospital and Gillispie said the report immediately after the game was that his vital signs were strong. Harris had missed five games with a back and neck injury sustained in a collision with a teammate on Dec. 3 against Lamar, but had played significant minutes in the last five games.
"We just wanted to get the win," Stevenson said. "We knew he wanted us to keep on playing and get the win."
The incident caused a delay to start the second half, and Gillispie missed the beginning to remain with Harris.
"It's a serious deal when a guy faints," the coach said. "He threw up and they said after that they started thinking he was feeling a little bit better. He had a little shortness of breath to start, and that's what concerned them the most."
Meeks continued his scoring tear to help Kentucky overcome that scare and an off game by Patrick Patterson, remaining the league's only team without an SEC loss. Patterson returned after a long absence due to foul trouble and quickly hit a pair of baskets to start an 8-0 run and give Kentucky a 55-47 lead with 3:36 left.
Alabama (12-7, 2-3) couldn't come closer than six points after that and missed 5-of-6 free throws down the stretch.
DeAndre Liggins scored 11 for the Wildcats off the bench.
The Wildcats held Alabama to 29 percent shooting. JaMychal Green led the Tide with 15 points, but guards Alonzo Gee (eight points), Senario Hillman (nine) and Mikhail Torrance (zero) were a combined 6-of-30 shooting and got few open looks.
"We didn't make enough shots, we didn't get enough good shots and we turned it over 14 times in the second half," Alabama coach Mark Gottfried said. "That was the difference."
Torrance had averaged nearly 23 points over the last three games since replacing injured point guard Ronald Steele, who announced Tuesday that he was leaving the team. He missed all eight attempts from the floor.
"I just think he kind of had one of those days," Gottfried said. "He had some pretty good looks. I thought his 3s were good looks. He just seemed to have one of those days where he didn't play as well as he has. That's going to happen sometimes."
Meeks took care of much of his team's scoring, including 18 of Kentucky's first 28 points extending into the second half.
The nation's No. 3 scorer, he made 10-of-18 shots and had nine rebounds. The rest of his team was just 9-of-31. He also made all but one of the Wildcats' four 3-pointers.
The 27 points didn't seem so bad considering Meeks had twice that many three games earlier at Tennessee.
"Alabama did a great job of denying me the ball," Meeks said. "We really picked up the defensive pressure in the second half. The defensive pressure opened up the offense. We got some steals and baskets in transition."
Patterson picked up three quick fouls in the first four minutes after halftime, but Alabama couldn't take advantage of his time on the bench to keep the lead. He finished with six points and five rebounds in 27 minutes.
"We don't want Patrick to be on the sidelines, but there are going to be times when it happens," Gillispie said. "In my opinion, he's an All-American and even in games he doesn't score, he demands respect, demands at least 1 1/2 players to guard him because of how hard he works. His numbers don't always indicate how good he is."
Alabama did manage to hold Kentucky to 38.8 percent shooting, well below its 51 percent average that ranked No. 2 nationally.
"When you go on the road and shoot 38 percent and win, that shows you an awful lot about the toughness of your team," Gillispie said.