With the likes of Priyank Panchal, who has been in red-hot form this season, and skipper Parthiv Patel failing to get going, Gujarat were rescued by Chirag Gandhi and Rush Kalaria's seventh-wicket unbroken stand of 126.
At stumps, Gandhi and Kalaria were batting on 62 and 59 respectively.
Medium pacer Deepak Behera was the most successful bowler for Odisha, playing in their first quarterfinal since 2001, returning figures of 3/36 in 13 overs, while his partner Basant Mohanty picked up two wickets.
Opting to field, Odisha had Gujarat on the mat at 71 for six in 31 overs.
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The bulk of the damage was done by Behera, who dismissed Gujarat's top three batsmen, including that of Panchal, who has so far amassed over 1000 runs with four centuries, including a triple and a double hundred.
Bhargav Merai tried to stabilise the innings, but fell for 31 to Behera. Returning from national duty after a fairly impressive show in the Test series against England, Parthiv (12) too could not get a big one, making his way back to the dressing room after spending 73 minutes in the middle. Mohanty was the successful bowler on this occasion.
Earlier, lunch was taken 47 minutes early at the Sawai Man Singh Stadium, with Gujarat 39 for 2, due to concerns over the pitch that reportedly arose when Parthiv was struck on the arm by a rising ball.
Play resumed after ground-staff re-rolled the pitch, and Gujarat slumped further against the medium-pace of Behera, Mohanty and Biplab Samantray, before Kalaria joined Gandhi at the end of the 31st over of their innings.