The left-handed opener scored 109 not out and shared century partnerships with Mohammad Hafeez [ Images ] and Azhar Ali, as Pakistan piled up 259 for one by the close, a lead of 62 runs, at the Sheikh Zayed Stadium.
It was a patient innings by the 30-year-old Umar, who faced 296 balls and hit eight boundaries.
Resuming at the overnight total of 27 for nought, Hafeez and Umar put on 118 for the first wicket.
Hafeez was the more aggressive and struck eight fours and a six before falling just after lunch, trapped leg before for 75 by left-arm spinner Rangana Herath [ Images ].
Umar and Ali then put on an unbroken 141 for the second wicket and Pakistan now look like building a substantial first-innings lead.
Mahela Jayawardene [ Images ] failed to take a low catch when Ali, on seven, edged Herath to slip.
Sri Lanka's pacemen toiled hard on a lifeless pitch as edges several times fell short of fielders.
Pakistan play 'home' Tests in the Gulf region because of security fears in their own country.
The game is the first in a three-match series.
Sri Lanka (1st innings): 197 (A. Mathews 52 not out, J. Khan 5-38)
Pakistan (1st first innings): (overnight 27-0)
M Hafeez lbw b Herath 75
T Umar not out 109
A Ali not out 60
Extras: (b-3, nb-12) 15
Total: (for 1 wicket - 98 overs) 259
To bat: Y. Khan, Misbah-ul Haq, A. Shafiq, A. Akmal, U. Gul, A. Cheema, S. Ajmal, J. Khan.
Fall of wicket: 1-118
Bowling: Welegedara 16-1-56-0, Lakmal 13-3-58-0, Herath 35-10-55-1, Pradeep 15-0-57-0, Dilshan 19-6-30-0.