Faheem Ashraf marked his Test debut with 61 not out and teenager Shadab Khan, in only his second match at this level, also hit a maiden Test fifty to be unbeaten on 52.
Murtagh had two for 30 in 14 overs, Rankin two for 33 in 14 and Thompson a slightly more expensive two for 47 in 13, with Ireland opting against including a specialist spinner in their XI.
Azhar Ali faced the first ball of the match from Tim Murtagh and kept out a yorker before calling his opening partner through for a single.
Former England global Rankin had the honour of taking Ireland's first-ever Test wicket when Azhar Ali (4) edged him to second slip in the grounds of Malahide Castle, just north of Dublin.
The ball had travelled just a couple of feet from the stumps and wicket-keeper Niall O'Brien and fielder Tyrone Kane both darted towards the ball while Ul-Haq, on Test debut, dived to make his ground.
The Irish are the 11th nation to play the longest format of the game after the International Cricket Council awarded Ireland Test status in June previous year. Barely had the crowd's cheers subsided, then Pakistan were 13 for two off the very next ball, with Imam lbw for seven to a Murtagh delivery that came back into him. The duo added 58 runs for the third wicket to allay fears of an absolute collapse, but Sohail's fall only reignited the possibility.
After a brief delay, Imam was able to carry on, with no wicket lost.
After the first hour, Pakistan were 22 for two, but they enjoyed a far better second hour as Haris and Asad Shafiq upped the scoring rate, putting on 54 runs as the pitch showed that any help for the bowlers will be minimal.
But with the towering Rankin, bowling from around the wicket, a similar shot proved Shafiq's undoing when he found Andrew Balbirnie at square leg.
But Shadab Khan (52 not out) and Faheem Ashraf (61no) excelled before play stopped again to put a dampener on another soggy day for Ireland. And when Pakistan captain Sarfraz Ahmed (20) was caught by Stirling in the slips off Thompson, the tourists were 159 for six.
Bad light saw the players leave the field at 5:27pm local time (1627 GMT) and 20 minutes later, after a thunderclap and a heavy downpour, play was abandoned for the day.