Australia, who won the toss and batted first, were all out for 157 in 42 overs, their lowest ODI total in Pakistan, with Inglis lashing a stand-out 65.
But It never quite looked like being enough to seal the winner-takes-all encounter in Lahore and Pakistan eased to victory - and an overall 2-1 success - with four wickets to spare.
Inglis said: "A bit like the first game (when Australia were bowled out for 200) we were just too many runs short. I thought the bowlers and the fielding group, in particular, made a great effort to put us in a position to potentially win the game, but it wasn't to be in the end."
After the start of the match had been delayed by 15 minutes because of a brief downpour, the hosts struck early. Shaheen Shah Afridi, who ended with figures of three for 30, had Matt Short caught at mid-on with the second ball of the innings.
However, there was always Inglis. Replacing Alex Carey as opener for the first time in the series, batted fluently, smashing Afridi for boundaries, then punishing Arafat Minhas with a muscular drive for four and a monstrous inside-out six over the covers.
Inglis profited on the offside, reverse-sweeping to good effect against the Pakistan spin but his team-mates found the going a whole lot tougher.
Manus Labuschagne has toiled in ODIs and his contribution to this vital encounter was cut short by a bizzare and costly mix-up in the 12th over when Inglis did not return his call for a second run and he was left exposed to Minhas's direct hit from the non-striker's end.
Carey, who like Labuschagne had contributed 19 opposite Inglis, fell victim to one that nipped in and took his middle stump.
That sparked a collapse that saw Inglis and Cameron Green depart within three balls of each other to catches off the bowling of Afridi.
The Aussies subsided from 3-98 to 7-131, with the loss of Matt Renshaw, their best batter on the tour, caught at slip by Salman Ali Agha for just four a grievous blow.
Adam Zampa was the only tail-ender to reach double figures. He got to 10 before Shadab Khan ended his stay with one that stayed low.
When Pakistan came to reply, the Australian bowlers had no intention of going meekly. They could even dare to dream when Nathan Ellis sent back Sahibzada Farhan and Short removed Maaz Sadaqat to leave the hosts on 2-41.
When Kuhnemann got to work, spinning a web around the batters with a tremendous three-wicket haul, including the prized wicket of Babar, clean bowled, who had top-scored with 40, Pakistan knew they still had work to do against Aussie spin on a turning wicket.
Abdul Samad and Shadab Khan rose to the occasion, showing great composure to stitch together a crucial unbeaten 49-run stand to finish the job in style.
Afridi, the Pakistan captain, said: "It was a complete team effort throughout the series. The conditions were tough for the batters, but every run counted and the players put in a great effort. All our bowlers executed their plans well, and the credit goes to them."
Pakistan had won the opening game in Rawalpindi by five wickets but when the action switched to Lahore on Tuesday, Australia levelled matters up with a 41-run victory to set the stage for Thursday's showdown.
It was Pakistan's third successive 2-1 ODI series victory - two at home, one away,- over Australia.
