Odorizzi pitched one-hit ball, but the Rays lost Zobrist to a dislocated thumb during a 2-0 win over the Seattle Mariners on Wednesday.
Zobrist's injury isn't considered serious. But the Rays are not sure whether he'll end up on the disabled list or be able to play through the injury. Rays manager Joe Maddon said the club would likely make a decision on Thursday after seeing how the thumb responds.
''We're getting different opinions. I think a lot of it has to do with how sore he is tomorrow, how swollen and sore,'' Maddon said. ''That could indicate DL. That could indicate maybe not.''
Zobrist hurt his left thumb on a headfirst slide while trying to steal second base in the fifth and yelled in pain.
The valuable all-purpose player jammed himself into the bag after being tagged out, walked off the field holding his hand and later had his thumb adjusted back into place. Zobrist said having the thumb put back in hurt more than jamming it originally.
X-rays to check if there was a fracture were negative.
''I guess best case scenario is it heals very quickly and I can get back on the field, maybe within a week,'' Zobrist said. ''That's unlikely I think and I think they're trying to decide whether I need to go on the DL or not. We'll see what decision is made.''
Odorizzi (2-3) picked up his first win since the opening week of the season, teaming with three relievers on a combined two-hitter.
Odorizzi allowed only two baserunners, both on walks, and then retired 12 straight batters before James Jones broke up the no-hit bid with a two-out single in the sixth.
Odorizzi struck out Stefan Romero to end the sixth, his eighth, but his pitch count was at 95. Odorizzi said he knew he had a no-hitter going but realized it was a long time before it could become reality.
''If I would have gotten through that sixth inning there are still nine outs to go. That's a lot of outs. I don't think you really think about it until it's like the eighth inning and you have an out or two,'' Odorizzi said. ''The hit we gave up was on the pitch we wanted too.''
With the Rays bullpen rested after Price's complete game the night before, Maddon ended Odorizzi's day after six innings. Jake McGee walked Robinson Cano to open the seventh, but got Justin Smoak to ground into a double play.
Joel Peralta worked around a one-out double by Dustin Ackley in the eighth, helped by a questionable strikeout of John Buck when he was called out by first base umpire Lance Barksdale on a check swing. That set off Seattle manager Lloyd McClendon. His argument led to his second ejection of the season and left a fan with a souvenir after McClendon threw his hat into the stands.
''It is what it is,'' McClendon said. ''You write what you saw. If I tell it, I get fined.''
Grant Balfour worked the ninth for his seventh save in eight chances.
Maurer failed to make it through that inning after losing command. With a runner already on base, Maurer issued three straight two-out walks to Myers, Brandon Jennings and the last to Escobar that forced in a run.
Reliever Dominic Leone almost immediately threw a wild pitch that scored Myers.
NOTES: Rays won consecutive games for first time since May 1-2. ... Seattle LHP James Paxton (back) threw a 52-pitch bullpen session on Wednesday. Paxton hopes to throw a simulated game this weekend on the road. ... Seattle SS Brad Miller committed his seventh error. He had seven errors in 68 games at SS last season.