Paceman Tim Murtagh took two wickets for 33 runs from 17 overs, with Boyd Rankin returning figures of two for 58 in 17.
Ul-Haq, nephew of legendary Pakistan captain Inzamam, did not appear to suffer too many after-effects although it did take him 16 balls to get off the mark before he drove Murtagh stylishly for four through the off side.
After rain played the spoilsport on Day 1 on Ireland's Test debut against Pakistan, it is a bright and sunny day, to begin with on day 3 at the Mahalide Stadium, Dublin.
No longer just constrained to the one-day game, Ireland's enthusiastic fans will at least get four more shots at enjoying Test cricket for the first time.
Pakistan opener Azhar Ali attempted to scoot through for a quick single and Imam-ul-Haq, the nephew of former worldwide batsman Inzamam, collided with Niall O'Brien, forcing a delay while he was attended to.
Pakistan opener Azhar Ali fended it into the legside and called for a quick single, but in scrambling through, debutant Imam-ul-Haq was clattered accidentally by Niall O'Brien and Tyrone Kane.
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The side winning the toss has opted to bowl in all 12 matches at Eden Gardens since IPL 2017, and have won 66.67% of those games. However, his innings was halted by Chawla on an individual score of 18 runs off 13 deliveries in the sixth over of the innings.
The 22-year-old left-hander was left flat on the ground and needed several minutes' treatment on the field.
Mohammad Abbas took 4-44 as Ireland were bowled out for 130.
Ireland's historic first Test wicket was actually Rankin's second in Tests though, his first came in his solitary England Test appearance against Australia in Sydney, during the 2013/14 Ashes.
Imam did not last much longer as he departed the next ball, leaving Ireland jubilant and Pakistan in trouble at 13-2.
Asad Shafiq had looked at ease until he pulled a delivery from Rankin straight to Andrew Balbirnie at square leg to depart for 62 and leave Pakistan five down. Sarfraz Ahmed, the Pakistan captain, was walking slowly and disconsolately towards the pavilion and Stuart Thompson, the Ireland seamer, was being mobbed by his team-mates.
Faheem, however, did have a break when, on 36, he edged Rankin only for a diving Niall O'Brien to miss the catch and give Gary Wilson at first slip no chance of taking the ball. Paul Stirling, with the match ball raised high in his right hand after a sharp catch, was hailing the noisy supporters at the Malahide Castle end of Test cricket's newest venue.