The all-rounder was unbeaten on 120 when Ricky Ponting declared Australia’s second innings on 225-8 in Melbourne.
Left-arm seamer Mohammad Aamer was the pick of the bowlers, collecting his first five-wicket Test haul with 5-79.
Salman Butt (33) and Faisal Iqbal (48) made useful starts as Pakistan finished the day on 170-3, with Mohammad Yousuf (45) and Umar Akmal (27) unbeaten.
The duo shared a 54-run fourth-wicket partnership in the final session, but will need to occupy the crease for most of the fifth day to stand any chance of overhauling a world record fourth innings target.
West Indies currently hold the record, successfully chasing down 418 to defeat Australia in Antigua in 2003.
With the free-flowing Akmal at the crease, alongside his obdurate captain Yousuf, Pakistan still have a fighting opportunity to create history.
But with left-arm seamers Mitchell Johnson and Dough Bollinger reverse swinging the 45-over ball, and Nathan Hauritz extracting discernable turn from a wearing MCG pitch, Australia are still on course for their third victory in four Tests.
Teenager Aamer was the star of the morning session, taking three wickets in the space of 16 balls to leave Australia reeling at 161-6.
Michael Clarke (37) was the first to fall caught behind by Kamran Akmal, while Marcus North was bowled for eight before Brad Haddin was dismissed for a duck, his first in Test cricket.
The 17-year-old became the second youngest Test bowler to collect a five-wicket haul – compatriot Nasim-ul-Ghani holds the world record aged 16 years 303 days following his 5-116 against West Indies in 1958.
Johnson provided Watson adequate support as he reached the 90s, but the opener suffered a series of wobbles as he neared three figures.
And the 28-year-old Queenslander was fortunate to reach the landmark when he was dropped on 99 by Abdur Rauf at backward point, but, after taking advantage of the misfield, stole a quick single for his first century in 15 Tests.
The 100 was Australia’s first since Michael Hussey’s innings in the fifth Ashes Test at The Oval in August.
And Johnson achieved his own milestone when he became the fifth player in history to score 500 runs and take 50 wickets in a calendar year. Only all-round greats Ian Botham, Kapil Dev and Richard Hadlee, who all achieved the feat twice, and New Zealand captain Daniel Vettori, who did it last year, have accomplished the double.
Australia captain Ricky Ponting declared for the second time in the match when Hauritz was stumped by off-spinner Saeed Ajmal, giving his bowlers almost four sessions to bowl Pakistan out.
Doug Bollinger gave the hosts the perfect start when opener Imran Farhat was adjudged lbw on referral following an initial not out decision by Rudi Koertzen.
Salman Butt and Faisal Iqbal put on 62 for the second wicket before the former was trapped leg before by Johnson with the score on 80-2.
And Iqbal fell two runs short of a half century when he was bowled attempting to cut a Hauritz delivery which turned sharply from the left-armer’s seamers.
Umar was dropped on 19 when he flailed a short delivery from Simon Katich to Hauritz, but survived through to the end of play.
