Pakistan were bowled out for 359 in their second innings with paceman Suranga Lakmal taking a career-best 4-78 on the fifth and final morning, giving Sri Lanka a target of 137 to win in 80 overs.
Lunch
Sri Lanka reached 35-0 at lunch as they chased the meagre target of 137.
The weather in Dubai was cloudy and rain was forecast for later Sunday.
At the break ,openers Dimuth Karunaratne and Kaushal Silva were at the crease.
Pakistan's lowest defended target was 127 achieved against New Zealand at Hamilton in 1993, when they dismissed their opponents for 93.
In a surprise move Pakistan opened the bowling with off-spinner Mohammad Hafeez but they failed to take any wickets.
Pakistan's batting
Earlier, Lakmal finished with a career best 4-78 as Pakistan lost their last three wickets for 29 runs to be bowled out for 359.
Lakmal removed Sarfraz Ahmed in the fourth over of the day, bringing one in sharply to beat the Pakistani's forward defensive push and hit the off-stump. Sarfraz scored 74, batting for 211 minutes and hitting seven boundaries in a fighting innings that took the game to the final day.
Lakmal then had Rahat Ali caught behind for eight, for Prasanna Jayawardene's ninth catch in the match. Prasanna equalled Sri Lanka's record of nine catches by a wicketkeeper in a match set twice in successive Tests by Amal Silva against India at home in 1985.
Lakmal bowled Saeed Ajmal (21) to end Pakistan's second innings. Lakmal's previous best was 3-55 against Australia at Galle in 2011.
Nuwan Pradeep, Shaminda Eranga and Rangana Herath took two wickets apiece.
The third and final Test starts in Sharjah on Thursday.
Scores:
Sri Lanka: 388 (Mahela Jayawardene 129, Kaushal Silva 95; Junaid Khan 3-102) and 137-1 (Kaushal Silva 58, Dimuth Karunaratne 62 not out)
Pakistan: 165 (Khurram Manzoor 73; Rangana Herath 3-26, Nuwan Pradeep 3-62) & 359 (Misbahul Haq 97, Younus Khan 77, Sarfraz Ahmed 74; S Lakmal 4-78).
COMMENTS (5)
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Ajmal is getting old and no longer effective. Rehman is a club bowler. Time to drop both in test cricket and introduce the leg spinning sensation, Usman Qadir.
@Commentator: We had 2 W's that time !!!
We need more players like Cpt. Tuk Tuk to stay on the crease.......!!
We lost because Misbah failed to complete his century and Saeed Ajmal didn't took early wickets. But this is also truth that these two play Test Cricket and rest of the 9 just assist them
Pakistan has successfully defended a score of 127 runs against Newzealand in 1993 and has managed to draw a test Match against England in 1987 when they given the target of 124 runs. Now it is 135 but I think we will lose this match.