But Lahiri was somewhat disappointed at his two-under round that took him to seven-under and he was five off the lead.
Lahiri, who began the week with a 65 and then followed it up with a 70 in a broken-up second round. On Saturday, he first came out and played six holes to complete his second round and then shot 68 in the 18 holes of the third to get to 203 on the Par-70 Colonial Country Club.
Meanwhile, Ryan Palmer shot 66 and was just one shot off the lead. Spieth was 12-under and Palmer was 11-under.
Spieth has now had rounds of 67, 66 and 65, improving by a shot with each round to be 12-under 198, while Palmer with 66, 67 and 66 is 11-under 199.
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Lahiri stuck to his task and discipline of finding fairways and greens and was cruising at three-under through first 10 holes. He was inside top-five and then after a bogey on 12th, he exchanged two birdies with two bogeys, as he gained shots on 16 and 18, but dropped shots on 15 and 17th.
Spieth's 65 came despite missing a lot of fairways and a few greens, while Palmer overcame consecutive early bogeys to shoot 66. He hit only three of 14 fairways and 11 of 18 greens in regulation.