Suleman was dismissed after scoring 86, while Ali returned unbeaten on 83 as Pakistan Shaheens achieved the 222-run target in 53 overs.
Earlier, Test fast bowler Khurram Shahzad picked up the last Sri Lanka wicket on the fourth ball of the day without any addition to the overnight score of 364 to finish with impressive figures of five for 70 and match figures of nine wickets for 102 runs.
Mohammad Suleman and Ali Zaryab had joined hands after Pakistan Shaheens had slipped to 32 for two following the departures of Mohammad Huraira (9) and Abdul Faseeh (22).
When Suleman departed at the score of 190 after hitting 11 fours in a 129-ball knock with Shaheens requiring 32 runs for victory, Haider Ali belted two sixes and a four in a rapid 14-ball 19 not-out.
Ali returned 83 not out from 125 balls with 11 hits to the fence. The highly-rated batter had scored 55 in Pakistan Shaheen’s 258 in response to Sri Lanka ‘A’ 115.
While Suleman and Ali took the second innings honours, Test fast bowler Khurram Shahzad was in sparkling form throughout the match.
In his third competitive match since returning from injury after successful completion of his rehabilitation at the National Cricket Stadium, the fast bowler returned figures of 10.1-3-32-4 and 25.4-4-70-5.
Khurram’s fellow new ball partner, Kashif Ali, also had a good match, recording figures of five for 31 and two for 79.
The second and last four-day match between Pakistan Shaheens and Sri Lanka ‘A’ will be played at the Rawalpindi Cricket Stadium on 18 November.