The Scottish bowlers failed to claim the quick wickets they wanted as the hosts advanced their overnight score of 285-7 to 404 all out.
PNG then claimed four wickets to leave the Scots 215 runs behind at the close.
Skipper Kyle Coetzer said: “We didn’t manage to make many chances today and they batted well. Conditions are great for batting so, hopefully, we can build a few big partnerships and look to get a first innings lead.
“We’ll try to bat most of the day and put them under pressure in the second innings.”
PNG’s eighth-wicket pair, who had already put on 32 on Sunday, added a further 61 runs yesterday morning.
Chris Sole finally made the breakthrough when Chad Soper edged to Matthew Cross to depart for 60. But there was further dogged resistance from Norman Vanua and Damien Ravu, who made 64 and 32 respectively.
Safyaan Sharif was the pick of the bowlers with four wickets, while Ali Evans and Michael Leask had two apiece.
Scotland made a solid start before Coetzer departed for 24 with the total on 64. His opening partner, George Munsey, went on to 53 with ten boundaries, while Calum MacLeod made 49.
Meanwhile, Rangana Herath made history as the first left-arm spinner to reach 400 Test wickets as Sri Lanka bowled Pakistan out for 114 to pull off a remarkable 21-run win in Abu Dhabi.
Sri Lanka’s hopes of inflicting a first defeat on the hosts at the Sheikh Zayed Stadium appeared slim after they were bowled out themselves for 138 and could therefore set Pakistan only 136 to win.
But veteran Herath (six for 43) and his fellow finger spinner Dilruwan Perera (three for 46) had other ideas.
Sri Lanka resumed on 69 for four on the final morning and doubled that total for the loss of their last six wickets as leg-spinner Yasir Shah (five for 51) did most damage. Niroshan Dickwella remained defiant, however, and when Pakistan’s batsmen then hit almost immediate trouble it became clear the Sri Lanka wicketkeeper’s unbeaten 40 could well be significant.
So it proved as Herath finished the match with his 400th wicket when number 11 Mohammad Abbas was last out lbw. The second and final Test in Dubai starts on Friday.
South Africa made short work of Bangladesh early on the final day of the first Test to complete a 333-run victory at Potchefstroom.
Faf du Plessis’ men were without injured seamer Morne Morkel, who will miss the second Test with a side injury, but ran through the tourists nonetheless, as left-arm spinner Keshav Maharaj (four for 25) and fast bowler Kagiso Rabada (three for 33) did the damage in a total of 90 all out.