Koronka pitched a career-high eight innings to win his third straight start and the left-hander got some big help in the third inning as Texas beat the Tampa Bay Devil Rays 8-3 on Sunday.
That was more than enough to support Koronka (3-1), who allowed five hits and struck out eight. He allowed only one hit after the third inning.
"I would say there were some unknowns about him," manager Buck Showalter said of Koronka, who was acquired March 31 from the Chicago Cubs. "I've been pleased with the progress he's made."
The Rangers, who have won eight of 10, completed a three-game sweep of the Devil Rays. Texas had 14 hits.
Jonny Gomes hit his ninth home run for Tampa Bay, which has lost five of six on its nine-game trip. Gomes, who homered in the sixth off Koronka, has four homers in his past four games.
In his last three starts, Koronka has 3.18 ERA. The 25-year-old had never gone longer than six innings.
"We don't expect him to go eight innings every night." Texas second baseman Michael Young said. "But if he keeps us in games as the No. 5 starter that's going to be big."
All three Texas homers in the third came off starter Casey Fossum. It was the first time the Rangers have hit three homers in an inning since July 27, 2005.
Teixeira hit his third homer of the season -- a three-run shot to put Texas ahead 4-2. Nevin hit his sixth two pitches later and Mench added a two-run blast to give Texas a 7-2 lead.
Mench has homered in three straight games and has 12 RBI over his past four games.
All Mench could do was shrug his shoulders after the game when asked about his hot streak.
"I can't answer that question," said Mench, who did not have an RBI in Texas' first 15 games. "I'm just trying to get back to the comfort level I found in spring training."
Fossum (0-1) allowed eight runs and 10 hits in four innings.
Tampa Bay starters came into Sunday's game with a 6.35 earned-run average. That ranked 13th in the American League.
"It's just one of of those things you have to program yourself to not worry about," Tampa Bay's Carl Crawford said. "It's no reason to jump on our starting pitchers. We just have to go out and score more runs."
Hank Blalock had three hits, including his fourth homer in the second off Fossum. Nevin added an RBI double in the fourth.
The Rangers scored 27 runs and hit seven homers in the three-game sweep of the Devil Rays.
Tampa Bay has been outscored 88-40 in the first five innings of games this season.
"It's always hard to have to come from behind," Tampa Bay manager Joe Maddon said. "It can wear you down. We as a group have to stay away from the big inning."
Damon Hollins put Tampa Bay ahead 1-0 in second with his third home run off the season.
Jorge Cantu extended his hitting streak to 10 games with an RBI double in the third.
Young went 0-for-4 and saw his 10-game hitting streak end. ... Gomes is one short of tying the Tampa Bay record for home runs in a month. Jose Canseco (April 1999) and Aubrey Huff (May 2003) each hit 10 in a month. ... Tampa Bay first baseman Russell Branyan struck out four times. He has 14 strikeouts in 36 at-bats.