CHICAGO (AP) -- Jose Abreu says he didn't expect this much success, especially in cold weather.
Yet he set another rookie record on Sunday.
Abreu, who had a two-run home run in the sixth and a two-run single in the seventh, has 31 RBIs to lead the majors. Albert Pujols had the previous rookie RBI mark of 27 in 2001.
Abreu's homer was his major league-leading 10th and extended his own record for home runs by a rookie through April.
''I go to the field to play baseball, help the team,'' Abreu said through a translator.
''I really don't go looking for records, but they're definitely welcome. That's not something that I go looking for, but it's a nice thing.''
Another White Sox rookie had a memorable day.
In his major league debut, Scott Carroll (1-0) gave up two runs, one earned, in 7 1-3 innings after he was called up from Triple-A Charlotte to fill in for injured ace Chris Sale.
Carroll, 29, received a standing ovation when he exited the game, and he planned to celebrate with more than 30 friends and family members.
''I couldn't have asked for a better showing,'' Carroll said. ''I know I was capable of it, but it's just awesome to finally get the opportunity and showcase my skills here at this level.''
Rays starter David Price (3-2) allowed eight runs, six earned, in six innings.
Trailing 1-0, the White Sox scored five runs in the sixth and four runs in the seventh.
The Rays committed four errors in the sixth. Gordon Beckham reached on an error and scored from second when Price threw away the ball after fielding Marcus Semien's bunt single. Adam Eaton scored when right fielder Wil Myers fumbled the ball after Price's throwing error.
Abreu then hit a two-run home run for a 4-1 lead. He set the rookie record for homers by the end of April on Friday with his ninth - a walk-off grand slam against the Rays.
''He's pretty strong,'' Rays manager Joe Maddon said. ''I've been talking about how impressive he's been this series. He is good. He's gonna get better.''
Dayan Viciedo doubled and scored on shortstop Yunel Escobar's throwing error for a 5-1 lead.
''It's very unusual. It's uncharacteristic of us to make those errors, but we're human, and I still feel like I have eight Gold Glovers out there whenever I'm out there on the mound,'' Price said. ''We have those days, and it stinks.''
Semien doubled to extend the White Sox lead to 6-1 in the seventh.
Abreu hit a two-run single and Ramirez added an RBI single for a 9-1 lead.
The Rays went ahead 1-0 in the fifth when David DeJesus singled and scored on right fielder Viciedo's error.
The Rays scored their second run in the eighth on Evan Longoria's single.
Before his call up, Carroll was 27-38 with a 3.95 ERA in 138 games during eight minor league seasons. He underwent Tommy John surgery in 2012 and bounced back with a 3-1 record and 1.57 ERA in four Triple-A starts this season.
''As soon as I found out I was going against Price, I thought to myself, 'What an opportunity,' " Carroll said. ''There's no better chance to showcase my skills and get to go against one of the best guys, a Cy Young winner. I just happened to be better than him today.
It's a fun experience, and I'm just so happy to do it.''
NOTES: Sale (forearm strain) played catch before Sunday's game, but when he'll return from the 15-day DL is uncertain. He is eligible to come off the DL on Saturday. ... To make room for Carroll on the 25-man roster, the White Sox optioned RHP Erik Johnson to Triple-A on Saturday. OF Avisail Garcia (left shoulder) was moved to the 60-day DL to make room for Carroll on the 40-man roster. ... Jake Odorizzi (1-2, 6.52) will start Monday for the Rays. Andre Rienzo (1-0, 4.91) will pitch for the White Sox.