Umar found another able partner in Younis Khan who was unbeaten on 25 at the break, the pair having put on 58 so far for the third wicket.
Sri Lanka, fighting hard to restrict Pakistan, managed just one wicket in the session when paceman Chanaka Welegedara bowled Ali with an incoming delivery in the seventh over of the day.
The overnight pair of Umar and Ali extended their second wicket stand to 160 as they again remained unflappable on a pitch that gave little response to pace and spin bowlers.Ali, who has 10 half centuries in 14 Tests now, yet again failed to register his maiden hundred as he came late on a swinging delivery which uprooted his off-stump. Ali struck six boundaries.
Younis had a shaky start as he was beaten by Welegedara first ball and was then dropped by Prasanna Jayawardene off skipper Tillakaratna Dilshan when a leg-side edge was dropped by the wicket-keeper despite getting two attempts.
Umar, 31, remained steady as he hit a glorious boundary off Suranga Lakmal and then took a single off Rangana Herath to go past his previous best score of 135, made on two occasions.
He hit 135 against South Africa at Cape Town in 2003 and repeated that score against the West Indies at St. Kitts earlier this year.
Umar has so far hit eleven boundaries during his 372-ball marathon innings.
The three-Test series is played at the neutral venues of United Arab Emirates after Sri Lanka turned down an invitation to tour Pakistan over security fears.