The hosts, replying to India's mammoth 675 for five declared, ended the third day's play on 364 for six, still needing 112 to avoid the follow-on with four wickets in hand on Tuesday.
Sachin Tendulkar clean bowled Moin Khan for 17 off the last delivery of the day to end a 43-run stand for the sixth wicket with Abdul Razzaq, who returned unbeaten on 47.
Inzamam, who hit a superb 77, was given out caught at short-leg off Anil Kumble by Australian umpire Simon Taufel on the third day even as television replays showed the ball go off the pad.
Pakistan were cruising at 233 for two on a wicket that remains a nightmare for bowlers before the captain's unfortunate dismissal in front of his home crowd before tea saw three more wickets fall by stumps.
Pakistan would have been in a worse position had Aakash Chopra not spilled a sharp chance at forward short-leg when Razzaq, on 39, tried to flick Kumble.
Razzaq will return on the fourth day to salvage his team's position in the company of tailenders.
A disappointed Inzamam trudged back slowly to the pavilion after the decision which ended a defiant stand of 160 for the third wicket with Yasir Hameed after Pakistan had been reduced to 73 for two in the morning session.
Hameed fell 10 runs later for 91, edging Irfan Pathan to wicketkeeper Parthiv Patel, giving the young left-arm seamer his 100th first-class wicket.
Pathan ended with 2-87 from 24 overs, while the remaining wickets were shared by Zaheer Khan, Kumble, Laxmipathy Balaji and Tendulkar.
Before India secured the Pakistan captain's scalp, they were given a taste of their own medicine as Inzamam and Hameed drove and cut fluently on the easy-paced wicket.
India had batted almost two days with Virender Sehwag scoring a triple century and Tendulkar left stranded on 194 not out when stand-in captain Rahul Dravid declared.
Inzamam, hoping to get a big knock in Pakistan's 300th Test match, hit 13 boundaries.
Hameed, who scored a century in each innings on his debut against Bangladesh last August, struck 14 fours.
Yousuf Youhana and Razzaq added 78 for the fifth wicket when Zaheer broke through by having Youhana caught down the leg-side by Patel for 35.
Pakistan, starting the third day on 42 for no loss, lost both the left-handed openers, Taufiq Umer and Imran Farhat, in the first hour.
Pathan moved one away from Taufiq, who hung his bat out and edged a catch to Dravid at first slip.
Farhat made 38 when Balaji, who replaced the expensive Zaheer, trapped him leg-before with his second delivery.
India, on their first full tour of Pakistan since 1989, won the preceding One-day series 3-2.