Pakistan, following on 268 runs behind, lost their top order in the post-lunch session of the fourth day to stumble to 91 for four in their second innings by tea on Wednesday.
The Indians, looking for their first Test win on Pakistani soil, seized the advantage despite losing strike bowler Zaheer Khan for the rest of the match with a muscle strain in the right leg.
Pakistan had added 22 to their lunch score of 11-0 when Imran Farhat was caught behind by wicketkeeper Parthiv Patel trying a big heave off Kumble.
It was soon 44 for three as India removed the other left-handed opener, Taufiq Umar, and captain Inzamam-ul-Haq in the space of five deliveries.
Umar was caught plumb in front of the wicket when he padded up to a top-spinner from the wily Kumble.
Inzamam, victim of a doubtful decision in the first innings after making 77, walked in to loud applause from some 5,000 fans on his home ground - only to be removed for zero.
He responded to a call from Yasir Hameed for a sharp single, but failed to make the striker's end as Yuvraj swooped on the ball at mid-wicket and threw down the stumps with a direct throw.
Yuvraj was at it again when, bowling left-arm spin, he claimed his first Test wicket as Hameed's pull shot was deflected off the close-in fielder's body to Virender Sehwag at fine-leg.
At tea, Pakistan's last recognised batting pair of Yousuf Youhana (19) and Abdul Razzaq (11) were at the crease.
Earlier, Pakistan were forced to follow-on in a dramatic collapse in the morning session after they began the day at 364 for six in reply to India's 675 for five.
The hosts lost their last four wickets for 43 runs to be bowled out for 407 after the first drinks break.
The total was boosted by a last-wicket stand of 36 between Mohammad Sami (15) and Shabbir Ahmed (19 not out).
Left-arm seamer Irfan Pathan finished with a career-best 4-100 in only his third Test after removing danger man Razzaq with the first delivery of the morning.
Razzaq, who was on 47 overnight, gloved a rising ball to the wicketkeeper.
In his next over, Pathan forced Saqlain Mushtaq to top-edge a skier to mid-off.
The 19-year-old Pathan's previous best figures were 2-80 against Australia at Sydney earlier this year.
Sachin Tendulkar, entrusted with bowling spin ahead of specialist Anil Kumble, took a return catch of Shoaib Akhtar as Pakistan slipped to 371 for nine.
Sami and Shabbir defied the Indians for an hour before Kumble terminated the defiant stand by bowling Sami.
Tendulkar followed his unbeaten 194 in the first innings with two wickets for 36 runs. Kumble had 2-100.
India have never won a Test match in Pakistan, having lost five and drawn the remaining 15.