Harrison went 5 1/3 innings, giving up 12 hits, seven runs and one walk.
It was the second consecutive subpar start for Harrison against the Rays. In his previous start against the team, in April, Tampa Bay collected 14 hits and six earned runs in another Texas loss.
Harrison knows that he has struggled against the Rays and is looking forward to getting another shot against them, as he is scheduled to start in St. Petersburg on Sept. 9.
"I have 26 hits against the same team in two games -- that's not very good," he said. "They had my number in the first two starts this year, but I guess I just need to make some adjustments and look at these two games, see what went well, what went wrong, and try to get better."
In the first inning, after Desmond Jennings scored on Ben Zobrist's double, Evan Longoria hit a two-run homer to put the Rays up, 3-0.
Tampa added on in the second inning behind a three-run homer from B.J. Upton to make it 6-0.
"Obviously, you have to stay on the fastball with a guy who has that kind of velocity," Upton said. "He's got that quick slide step, so I had to kind of preset myself and look for something to drive and put into play in that situation. He threw me something I could handle, and I took advantage of it."
Even though they fell to 77-53 on the season and saw their division lead shrink to 4 1/2 games because of the Athletics' win, the Rangers ended the 10-game homestand and their stretch of 20 games in 20 days feeling good about their status.
"I think, overall, we are right where we want to be," manager Ron Washington said. "We're playing good baseball, we just won three against Minnesota, won two out of three against Tampa Bay, and if we go into Cleveland and continue to win series, we'll be exactly where we want to be. The key is just to keep winning series. If we can get lucky and sweep series, everything will work out, but the key is just to keep winning series the rest of the way out."
Michael Young thinks that the team, which is three games ahead of last year's pace and four games ahead of the 2010 pace, is rounding into peak form just in time for September and October, having won nine of its last 12 games.
"On this homestand you saw a team that recognized that the stretch drive is right around the corner," Young said. "We said all along that we wanted to improve as the season went on, and we've done that, so we're looking forward to this road trip."
One of the few bright spots for the Rangers on Wednesday was reliever Koji Uehara, who threw 1 2/3 scoreless innings, with two strikeouts and a double play, in his second appearance since returning from the disabled list.
Washington said that this performance could go a long way toward getting Uehara back to where he was before he strained his right latissimus dorsi.
"It's going to be very important, because we consider him a winning piece," Washington said. "We were just trying to keep the game there. He came in and gave us 1 2/3 innings of pretty good baseball. The more we can get him in there and get him to face some hitters [after] the time that he's been out, the better off he's going to be. He's going to be a big piece as we move forward."
Mitch Moreland and Josh Hamilton each homered for the Rangers, who were able to cut the Rays' lead to two runs before solo home runs by Elliot Johnson and Longoria (his second) brought the game to its final margin.