Houston's Pedro Feliz hit a three-run homer off Price to make the score 4-0 with only one out in the first, and that was earned on a running catch by Zobrist, who snared a Carlos Lee liner that scored the first Astros run with the bases loaded.
"I was hoping not to go to the bullpen that early, because that can mess you up for several days," Rays manager Joe Maddon said. "But [Price] was able to right himself and get through five. He pitched well after that.
"The National League [rules] got him. The fifth inning was probably his best. I had to get him out of the game for the pinch-hitter."
That proved to be a good move by Maddon.
Willie Aybar, the pinch-hitter, singled in Reid Brignac in the top of the sixth to put Tampa Bay on top to stay. And five Rays relievers allowed only one run over the last four innings.
"The bullpen did a wonderful job again today," Maddon said.
Reliever Joaquin Benoit struck out the side in the sixth, giving him nine consecutive strikeouts spread over three appearances. Rafael Soriano got Hunter Pence for the final out to collect his 13th save.
Price looked perturbed by his performance, giving up five earned runs in as many innings to go with six hits and three walks. While he improved to 7-1, his ERA jumped from 1.81 to 2.41.
"They were hitting his fastballs," Maddon said. "Those things are going to happen. You can't pitch with that kind of effectiveness every time."
"I left some pitches up," Price said of the first inning, when he threw 41 pitches. "I didn't make pitches. It was just brutal. I didn't throw very well. It's always frustrating [to come out of a game]."
The Rays were surprised to see Price struggle in the first inning but knew what they had to do.
"That doesn't happen often," Brignac said of Price. "He battled through it. We knew it was early. We knew we could score some runs. Our guys came off the bench and hit."
The Rays have relied on their starting pitching most of the season to build their MLB-best 32-12 record. It is the best 44-game start to a season in the Majors since the 2001 Mariners opened the year with the same record.
"He did have a rough time getting [started], but he stayed tough," Zobrist said of Price. "To be able to come back that quickly and score 10 runs is a good confidence builder. It's a good team win."
Gabe Kapler, another pinch-hitter, opened the three-run eighth with a double to keep the Rays rolling.
Jaso, batting third, delivered a two-run homer in the fifth, tying the game at 4, and a two-run triple in the eighth that gave the Rays a four-run cushion.
"He blocked the ball well," Maddon said of his catcher. "He threw the ball well [cutting down Pence trying to steal in the seventh] and he hit the ball today."
"I've hit third before," said Jaso, although it was his first time doing as a Major Leaguer. "I tried to do the same as in the eight hole. All the way through the lineup picked it up."
The homer was Jaso's second in the big leagues.
"[Houston starter Bud Norris] had got me to pop up the at-bat before with pretty much the same pitch," Jaso said. "It was a fastball up and in. As a catcher I probably would have called the same thing."
Jaso was as surprised as anyone to see Price falling behind hitters from the beginning.
"His stuff in the 'pen, warming up, was unbelievable," Jaso said of his starting pitcher. "Some of the best I've seen. I know he was [upset] to come out of the game, but that's a good thing."
Tampa Bay supplied plenty of offense to back up Price, this time.
"We had a couple of big hitters out of the lineup, and everybody just stepped up," said Zobrist, who went 3-for-6.
Maddon gave third baseman Evan Longoria and shortstop Jason Bartlett the day off, starting Hank Blalock at third, moving second baseman Brignac to short and starting Sean Rodriguez at second. Blalock homered and walked twice.
"We still have 10 more games before our next day off," Maddon said. "If the schedule is not going to give you days off, then you need to do it on your own. I don't care what birth certificates say. If you keep them fresh, you stand a much better chance of them playing well in October.
"We're not looking for the next Cal Ripken right now. We've got a hundred games or more still to play. If you were to permit [Longoria to challenge Ripken's record] I bet that he could. I want to keep him well and healthy."