Jamshed's innings, which spanned just 98 balls and included 11 fours and two sixes, helped Misbah-ul-Haq's side make light work of what looked set to be a Testing target after Australia made 248 for nine.
The 22-year-old shared partnerships of 66 with fellow opener Mohammed Hafeez (23) and 101 with Azhar Ali before miscuing a drive at Mitchell Johnson to be caught at mid-off by Mitchell Starc just three runs short of his second ODI hundred.
Australia's bowlers were handicapped by heavy dew in the second innings of a match that spanned two days and finished in the early hours of the morning local time.
"It was a good toss to lose as dew was a major factor," Misbah said.
"It was good for us there was so much dew during the second innings but the way Nasser Jamshed played, he showed his class."
Australia captain Michael Clarke said on the eve of the match that he wanted bigger contributions from his batsmen but although five of them passed 20, only Mike Hussey (61) was able to reach a half-century.
He conceded, however, that it had been a mistake to bat first after winning the toss.
"It was definitely the wrong choice but we can't use it as an excuse," Clarke said.
"With the late start, dew will affect both sides so it's all about finding a way of executing better than we did tonight.
"A big part of the role of our top four is to make big scores and it's disappointing we weren't able to do that again."
Australia's batsmen were once again shackled by Pakistan's spinners with off-spinner Saeed Ajmal again proving the key bowler.
Ajmal, who took 3-30 in the previous match in the previous match in Sharjah, once again tormented the Australia batsmen and finished with 4-32.
"He's our number one bowler and he's the number one in the world," said Misbah. "He is playing his role, helping us win matches but the other spinners are doing that too."
Ajmal tormented David Warner (24) and the opener laboured for 68 balls before being put out of his misery when he tried to work the spinner on the on-side and was adjudged leg before wicket.
Ajmal also removed David Hussey lbw for a duck leg as he pushed forward and then returned later in the innings to dismiss Mike Hussey and Glenn Maxwell (28), the latter stumped as he charged a doosra after a bright knock.
Mike Hussey faced 72 balls and hit a four and two sixes as he and George Bailey (39) got Australia back on track with a stand of 66 in 14 overs after coming together with their team in some disarray at 87-4.
There were two late wickets for left-arm fast bowler Junaid Khan (3-52) but at the halfway stage Australia's total looked a useful one until it became apparent that dew would be such a handicap.
Asad Shafiq (9) fell cheaply soon after Jamshed was dismissed to give Australia hope but Azhar Ali (59 not out) and Misbah (35 not out) ensured there was no late wobble, adding an unbroken 59 from nine overs to see their side home.
The deciding match of the series will take place in Sharjah on Monday, with three Twenty20 internationals to follow.
- Mike Hussey