Updated

Chicago, IL (SportsNetwork.com) - Alexei Ramirez tied the game with an RBI triple in the fourth and scored the go-ahead run on Marcus Semien's double later in the frame, as the Chicago White Sox secured a 7-3 win over the Tampa Bay Rays in the finale of a four-game set Monday at U.S. Cellular Field.

Alejandro De Aza drilled a two-run homer in the second and after Semien put the White Sox in front in the fourth, Adam Eaton added some insurance with a two-run double in the sixth for the White Sox, who took three of four from the Rays.

"Taking the series is great," Eaton said. "You want to take three out of four from everyone, or two out of three, so we'll take it."

Jose Abreu collected his 32nd RBI of the season with a single in the eighth, extending his Major League rookie record for RBI in the month of April.

Chicago starter Andre Rienzo (2-0) recorded the win after yielding three runs -- two earned -- on five hits and three walks with four strikeouts over six innings.

David DeJesus smacked an RBI double for the Rays, who have lost five of their last six games.

"They beat us fair and square," Rays manager Joe Maddon said of the White Sox. "You just have to give them credit. They played well and they beat us."

Jake Odorizzi (1-3) got the start for the Rays and surrendered four runs on eight hits and two walks over 4 1/3 innings.

DeJesus' double provided the visitors with a 3-2 lead in the top of the fourth, but the White Sox answered swiftly in the home half, as Dayan Viciedo worked a leadoff walk before scoring when Ramirez followed with a triple that tipped off the glove of center fielder Desmond Jennings on the warning track.

Odorizzi nearly escaped with the game still tied after grounding out De Aza and fanning Tyler Flowers, but Semien smacked a two-out double to left and Ramirez trotted home for a 4-3 lead.

Eaton extended the margin with a two-out, two-run double to left in the sixth. Flowers kept the frame alive with a single and Semien walked before both runners scored on Eaton's two-bagger into the left-field corner.

Abreu's two-out single in the eighth scored Semien to account for the final margin.

Early on, the Rays jumped on Rienzo in the first, as Ben Zobrist smacked a leadoff double before Jennings put down a bunt that Rienzo bobbled. The Chicago right-hander then tried to throw to first from a knee, but his throw skipped past second baseman Gordon Beckham covering first.

Zobrist scored easily on the play, while Jennings was awarded second after running into Beckham on his way to second.

Matt Joyce followed with a drive to right-center field that Eaton snared with a leaping grab at the wall. Eaton fell to the ground after the catch and Jennings, who was tagging up on the play, raced around third before beating the relay throw to the plate to give Tampa Bay a 2-0 lead.

De Aza's two-out, two-run blast in the second tied the game. Adam Dunn started the inning with a single and moved to second on a bunt two batters later before crossing the plate on De Aza's fourth homer of the season.

Game Notes

Tampa Bay went 0-for-5 with runners in scoring position and finished the series 6-for-35 with RISP ... Chicago finished 4-for-12 with RISP and stranded nine runners ... Zobrist and Jennings each had two of Tampa Bay's seven hits.