The England stand-in captain was on 14 when he stepped out to drive spinner Harbhajan Singh and misread the line. But wicket-keeper Mahendra Dhoni failed to gather the ball, with the batsman out of the crease.
Flintoff was unbeaten on 19 with all-rounder Paul Collingwood (31) as England reached 138-5 in their second innings at tea on the fourth day for an overall lead of 259.
The pair added 53 crucial runs for the unfinished sixth wicket after their team had been reduced to 85-5 midway through the afternoon session here on Tuesday.
Flintoff also had a close shave when silly-point fielder Yuvraj Singh failed to hold a forcing shot off leg-spinner Anil Kumble before the batsman had opened his account.
England hearts again skipped a beat when a mistimed Flintoff drive fell just short of Kumble. But the visitors needed both luck and pluck to survive against the Indian spinners, who kept a tidy line and length.
England, seeking to square the series, found runs hard to come by as they made 54 in the first session and 53 in the second.
They lost three wickets after resuming on 31-2, with left-arm seamer Irfan Pathan and Kumble each getting one. Debutant Owais Shah was run out after contributing a solid 38.
Kumble took a superb return catch to dismiss Ashes hero Kevin Pietersen and Pathan removed defiant nightwatchman Shaun Udal, who had batted more than an hour to frustrate the hosts.
The leg-spinner, bowling round the stumps, moved swiftly to his left to hold an uppish drive to remove Pietersen for seven.
Udal had done his nightwatchman's job when he was caught low at second slip by Wasim Jaffer off Pathan. He had hit Shanthakumaran Sreesanth for two fours in the early overs before mistiming a drive.
Shah, who scored an impressive 88 in the first innings, batted more than a session before being caught short of the crease by Sachin Tendulkar's throw to the wicketkeeper.
India lead 1-0 in the series following their nine-wicket victory in the second Test at Mohali. The first match ended in a draw.