Mathews notched up 116 not out under pressure for his second Test hundred and put on invaluable 138-run partnership for the fifth wicket with Dinesh Chandimal (89) and 99 for the unfinished sixth wicket with Prasanna Jayawardene (48 not out) to take Sri Lanka to 420/5 at close at Sheikh Zayed Stadium.
Sri Lanka resumed the day at 186/4, but Mathews' career-best score and resolute innings by Chandimal and Prasanna helped Sri Lanka add 234 runs for the loss of only one wicket.
They now lead by 241 runs and with five wickets intact can harbour hopes of an unlikely win on the fifth and final day or at least salvage a draw.
Mathews batted with resolve, blunting off-spinner Saeed Ajmal and had the better of Pakistan's three-pronged pace attack, reaching his hundred in the final session, taking two off Bhatti. His hundred came off 239 balls.
In all the Sri Lankan captain batted for 370 minutes, hitting 12 boundaries and six off Ajmal, who conceded 96 runs in 42 wicket-less overs.
Neither Mathews nor Chandimal were bothered at all and even the second new ball, taken at 249/4, failed to benefit Pakistan with a wicket as Sri Lanka reached 285/4 at lunch.
Pakistan had one chance to dismiss Chandimal in the second over after lunch when a edge off Bilawal Bhatti flew close to Ahmed Shehzad's outstretched hands in the second slip when the batsman was 71.
Finally, Junaid broke the stand at 324 when he had Chandmial caught at deep fine-leg off a miscued hook. Chandimal batted for 251 minutes and hit a dozen boundaries.
But even after Chandimal's exit, Mathews and Prasanna batted without any problems to leave Pakistani bowlers frustrated.
Mathews's previous best of 105 not out came against Australia at Colombo in 2011 and followed up his 91 in Sri Lanka's first innings total of 204. Pakistan had made 383 in their first knock.
Prasanna has so far hit five fours and six in his able assistance of Mathews.
Left-arm paceman Junaid was the best Pakistani bowler with 3-81 while fellow fast bowler Bilawal Bhatti took 2-131.
Pakistan started the day on a wrong note when wicket-keeper Adnan Akmal was ruled out of the three-Test series with a fractured finger and Younis Khan had to keep wickets.
Sarfraz Ahmed has been summoned as Akmal's replacement for the next two Tests, second in Dubai (January 8-12) and Sharjah (January 16-20).
Brief scores
Sri Lanka 204 (Mathews 91, Junaid Khan 5-58)) and 420 for 5 (Mathews 116*, Chandimal 89)
Pakistan 383 (Younis Khan 136, Misbah-ul Haq 135, Eranga 3-38, Herath 3-93)
Status Sri Lanka lead by 241 runs
