McCullum was unbeaten on 100 -- his tenth century -- as New Zealand reached 164-1 at tea on the second day, 187 behind Pakistan's first-innings total of 351.
Kane Williamson was equally aggressive with 45-ball 44 not out as the duo punished a sloppy Pakistan attack during their 98-ball, 113 run, unbroken stand for the second wicket, lifting their efforts for a series-levelling win.
Pakistan lead the series 1-0 after winning the first Test and drawing the second.
This was the fastest hundred ever by a New Zealand batsman, beating the 81-ball hundred Ross Taylor made against Australia at Hamilton in 2010.
In all McCullum has so far hit 13 boundaries.
Earlier off-spinner Mark Craig took a career best 7-94 as Pakistan lost their last seven wickets for 70 runs to get bowled out for 351 after resuming at a strong 281-3.
Opener Mohammad Hafeez hit a career best 197 before he miscued a pull off leg-spinner Ish Sodhi and was caught at deep square-leg.
