The Indian vice captain's fifth double-century in Test cricket, and the third this season, fired the tourists to 600 in their first innings in reply to Pakistan's modest 224 on Thursday.
Pakistan, trailing by 376 runs on the first innings, were 49 for two in their second knock by stumps on the third day, still 327 runs away from avoiding an innings defeat in the decisive final Test.
Imran Farhat was caught in the slips off Laxmipathy Balaji for three, while Taufeeq Umar was given out leg-before to Irfan Pathan after making 13.
Yasir Hameed was unbeaten on eight and nightwatchman Kamran Akmal was on 10 as the hosts faced an uphill task to prevent India from winning their first overseas series since Sri Lanka in 1993 and their maiden one on Pakistan soil.
The archrivals are locked 1-1 in the three-match rubber, the first between the two countries in Pakistan since 1989.
Dravid, who came to bat on Tuesday evening after opener Virender Sehwag was dismissed off the first ball of the innings, grounded the Pakistani attack into the dust for two consecutive days.
He had batted through Wednesday to remain unconquered on 134 and continued in the same vein till an hour before stumps on Thursday to put India in control of the make-or-break Test.
Dravid held vigil for 12 hours and 20 minutes under the hot sun, hitting 34 boundaries and a six, before he was ninth out, bowled by part-timer Imran Farhat attempting an uncharacteristic reverse sweep.
It was the 31-year-old's third major knock in nine Tests this season following his 222 against New Zealand at Ahmedabad in October and 233 against Australia at Adelaide in December.
"Rahul has batted like the champion he is this season," said Indian coach John Wright.
"Can't ask for more really. It was nice to get those two wickets this evening and hopefully we will keep the pressure on Pakistan tomorrow (Friday). The wicket is wearing a bit, but we still need to take the remaining eight wickets. I don't care whether the match gets over on the fourth day or the fifth. There is a job to be done yet."
Pakistan badly missed strike bowler Shoaib Akhtar, who was confined to the dressing room the whole day with a ruptured back muscle, caused by a fall on his follow-through on Wednesday afternoon.
The absence of Akhtar, who had grabbed three of the first four Indian wickets, was a major blow to the injury-hit hosts already without second Test hero Umar Gul and fellow seamers Shabbir Ahmed and Abdul Razzaq.
Leg-spinner Danish Kaneria bowled 62 overs, conceding 178 runs for his two wickets, while Fazl-e-Akbar finished with 1-162 and Mohammad Sami 1-116.
Resuming at the overnight score of 342 for four, Dravid and captain Sourav Ganguly carried their sixth wicket stand to 131 when Pakistan earned a lucky break 25 minutes before lunch.
Ganguly, who looked in ominous form making 77, failed to ground his bat after completing a sharp single and was run out by a direct hit at the non-striker's end from Farhat.
Next man Yuvraj Singh put on 98 for the sixth wicket with Dravid before being trapped leg-before by Sami for 47 in the post-lunch session.
India won the first Test at Multan by an innings and 52 runs before Pakistan drew level with a nine-wicket triumph at Lahore last week.