Needing 15 runs off the last over on Wednesday, Moeen managed to hit just one six off debutant fast bowler Aamer Jamal to reach his fifty as England were restricted to 7-139.
Mark Wood's pace had earlier dismantled Pakistan for 145 in 19 overs. David Willey and Sam Curran both grabbed 2-23.
It was the second time in a row that England slipped up while chasing a below-par total in the seven-match series, which Pakistan lead 3-2.
England lost the fourth T20 at Karachi by three runs when Pakistan chipped in with the last three wickets for just one run.
Moeen made an unbeaten 51 off 37 balls here, but Pakistan strangled England through spinners Iftikhar Ahmed (1-16) and Shadab Khan (1-25) in the middle overs and the run-rate kept on climbing.
"Today was the most disappointing performance with the bat for sure," Moeen said. "I felt we needed two big hits, I managed to hit one ... but it was a very good last over and you can't take anything away from him (Jamal)."
Top-ranked T20 batter Mohammad Rizwan's belligerent form continued as he anchored Pakistan's innings with 63, his fourth half century in the series after Moeen won his fourth toss.
Pakistan's middle-order stumbled against Wood's pace, which got rid of captain Babar Azam with a steep short ball and then claimed the wickets of Haider Ali and power-hitter Asif Ali with sharp, short-pitched deliveries.
Pakistan slipped to 7-100 in the 14th over when Shadab was run out in a mix-up with Rizwan.
Rizwan also holed out at deep fine leg when he couldn't clear Curran's low full toss in the 18th over, before the returning Chris Woakes wrapped up the innings when Rauf was caught in the deep.
England slipped to 3-31 against pacers Rauf and Mohammad Wasim while Mohammad Nawaz had Alex Hales caught at point in his first over.
Shadab reduced England to 4-54 when he successfully overturned an lbw decision of in-form Harry Brook (4) in the ninth over.
Ahmed then ended Dawid Malan's nearly run-a-ball knock of 36 and Jamal got his first wicket off his second ball when Sam Curran holed out.
Moeen carried the fight with a 46-run stand with Woakes (10), before the latter fell to Rauf in the penultimate over. Then the 26-year-old Jamal bowled some superb yorker length deliveries to Ali in the last over to deny England victory.
"It's a team game and we believe if we are struggling (in one department), the other one (bowling department) chips in," said Shadab, who was playing in his first game of the series after missing out the four games at Karachi.
"Aamer Jamal had to believe in himself and we all backed him for the last over."
Lahore will host the remaining two games of the seven-match series on Friday and Sunday.
6°C