Having closed day one in Dubai on 219-4, Sarfraz (109), ably supported by an 89 from Asad Shafiq, pushed Pakistan to a first-innings total of 454 all out with his second five-day century in three months.
But, after enduring a somewhat difficult day in the field, Australia responded superbly with the bat, Warner and Rogers putting on their fifth stand of 100 in 21 matches together as the tourists reached 113-0 at stumps.
Captain Misbah-ul-Haq (69) and Shafiq set the tone for the day by adding 72 runs to Pakistan's overnight total before the skipper departed with an ill-fated attempt to smash a Steve Smith (1-50) delivery over long-off.
With Pakistan 291-5, Australia will have hoped to rattle through the lower order but were frustrated as Sarfraz and Shafiq combined brilliantly for a sixth-wicket partnership of 124.
Test debutant Steve O'Keefe (2-107) claimed his first Test wicket to deny Shafiq his hundred, but Sarfraz continued undeterred, reaching his century – which he brought up with a four over the slip cordon – in just 80 balls.
Yet the wicketkeeper found little in the way of support from the tailenders, with Sarfraz's departure at the hands Nathan Lyon (2-148) effectively signalling the end of Pakistan's innings as Zulfiqar Babar retired hurt after taking a blow on the hand from Mitchell Johnson (3-39) and Rahat Ali fell to Lyon for a duck.
Openers Warner and Rogers were undaunted by the total set by Pakistan and set about the task of bettering the hosts' mark with considerable enterprise.
Perhaps unsurprisingly it was Warner that lead the way with a typically quick-fire 75 not out from 77 balls, while the more patient Rogers contributed an unbeaten 31 from 110 deliveries, leaving Australia in a promising position with captain Michael Clarke and exciting Test debutant Mitchell Marsh still to bat.