Dinesh Chandimal (89) was the only man to fall on day four in Abu Dhabi as Sri Lanka progressed from 4-186 to 5-420 and a lead of 241.
Captain Angelo Mathews batted through the day for 116 not out, his highest score in Tests, sharing 138 with Chandimal and an unbroken 96 with wicketkeeper Prasanna Jayawardene (48).
Sri Lanka took a slender advantage of seven into the morning session after losing three wickets on the third evening, with Pakistan hoping for early wickets in order to set up a short run-chase.
However, Misbah-ul-Haq's side were left disappointed as Chandimal and Mathews combined to excellent effect prior to lunch.
Chandimal eventually departed in the afternoon, caught at deep fine-leg hooking Junaid Khan (3-81 off 31 overs).
Yet Mathews, who was content to rein in his aggressive instincts, continued to hold firm and found another willing ally in Jayawardene.
The skipper moved beyond his first-innings score of 91 and previous Test best of 105 not out, the latter score having been compiled against Australia in September 2011.
At stumps, Mathews had faced 282 balls, striking 12 fours and a six, while Jayawardene's innings spanned 107 deliveries.
Spinner Saeed Ajmal returned figures of 0-96 from 42 overs, the most he has bowled in a Test innings without picking up a wicket.
Pakistan have only ever successfully chased a target higher than 240 in the fourth innings of a Test on three occasions and may now have to battle to save a draw ahead of remaining matches in Dubai and Sharjah.