Dellucci led off with a home run for the second straight day and Park pitched seven strong innings, leading the Rangers over the Seattle Mariners 6-2 on Friday night.
The Rangers had their 37th multihomer game of the season after hitting eight in an 18-5 victory over the Los Angeles Angels on Thursday in Arlington. They lead the majors with 130 homers.
"They have a lot of big hitters in that lineup," Mariners manager Mike Hargrove said.
Hours after learning that Rogers was suspended 20 games and fined $50,000 by Major League Baseball for an outburst that sent a television cameraman to the hospital, the Rangers won their third straight game.
Rogers, whose suspension and fine are being appealed by the players' union, is with the team and is scheduled to pitch on Sunday against the Mariners.
Laynce Nix also homered and drove in two runs for the Rangers, who won for the third time in four games in Seattle in 2005.
The Mariners have lost six straight and seven of eight, dropping to a season-worst 12 games under .500.
Park (8-2) gave up two runs and five hits, walked three and struck out six. He threw 111 pitches.
Park had a 4-7 record in 16 starts in 2004, when he missed more than three months with a back injury. Against the Mariners, he made his 16th start of this season. He also was injured in 2003 and 2002.
"I'm healthy and that makes me much more different," Park said. "I'm comfortable. I'm getting more movement on my fastball and that helps me get more groundballs. I'm not thinking about the past now. I'm focusing on the future."
With a 419-foot shot to right field, Dellucci gave the Rangers a 1-0 lead on Aaron Sele's second pitch of the game. It was Dellucci's fourth leadoff homer of the season and fifth of his career. He has 14 homers this season.
"I think when you're leading off, you're just trying to see the pitcher and see what he's featuring for the day," Dellucci said. "You just want to put the ball in play. If the ball goes out of the ballpark, that's a bonus."
The Mariners tied it at 1 in the second inning on Jeremy Reed's RBI double.
Nix hit an RBI double and Richard Hidalgo had a run-scoring single in the fourth, giving the Rangers a 3-1 lead. Hank Blalock and Alfonso Soriano singled in runs for Texas in the fifth, and Nix homered off Sele (6-7) to lead off the sixth.
Ichiro Suzuki tripled and scored on Randy Winn's single for Seattle's second run in the sixth.
Sele pitched 5 2/3 innings, allowing six runs and nine hits.
"The job of a starting pitcher is to keep the game close and I didn't keep it close enough long enough," Sele said.
- Hidalgo ended an 0-for-17 drought with a single in the second.
- Park is 4-1 in seven starts at Safeco Field and 5-2 in his career against the Mariners.
- Suzuki had his eighth triple of the season, tying his career high set in 2001, 2002 and 2003.
- The Mariners have scored a total of 16 runs in going 0-6 after scoring 14 runs in their last victory June 24 in San Diego.