Pujara, who had stonewalled for 25 balls in overcast condition tapped before getting run out.
Pujara has now been involved seven out of the 10 Indian run-outs in the past few Test matches.
As inclement weather stopped play at 8.3 overs, skipper Virat Kohli remained not out on three. This was after Murali Vijay (0) and KL Rahul (8) were dismissed in the first session by James Anderson (2/6).
It was ironical that players were racing off the ground a ball earlier as it started drizzling only to be called back by the umpires. Off the very next ball, Pujara got run-out and play was halted immediately after that.
It was completely Kohli's fault as called and ran but said no mid-pitch after he spotted Olliver Pope converging on the ball.
Pujara was left stranded, albeit he tried making it to the non-striker's end, only to find that Kohli had backtracked and made the crease safely. Pope completed the formalities by whipping off the bails.
This was after Anderson took two wickets in the space of 15 balls as he sent the Indian top-order reeling in a 31-minute passage of play.
Under intense cloud cover, the Indian top-order had a testing time against Anderson and Stuart Broad (0-7).
Vijay looked to leave well, but played an uncharacteristic flick shot to a late outswinger from Anderson, and was bowled for a five-ball duck.
Rahul (8) left well against Broad and managed to score two boundaries as well. Leaving against Anderson though was a sterner challenge, as he nicked one in the seventh over and was caught behind.