Mehidy bowled a career-best 4-12 to help the hosts bowl out England for 117 before he hit 20 off 16 balls as Bangladesh raced to 120-6 in 18.5 overs.
Najmul Hossain top-scored at the Sher-e-Bangla National Stadium in Dhaka with 46 not out for Bangladesh, who have now won at least one series in one format against all Test-playing countries.
"In a tricky game like this it was important to keep our nerve. Shanto... Mehidy, a superb innings for the team," Bangladesh captain Shakib Al Hasan said.
The hosts won the first match of the series by six wickets in Chittagong.
Sent into bat first, England were rarely in the contest after losing their way in the middle of the innings as their batsmen struggled to cope with a low and slow wicket in Mirpur.
Shakib Al Hasan, Taskin Ahmed, Hasan Mahmud and Mustafizur Rahman each complemented Mehidy with a wicket apiece.
Ben Duckett top-scored with 28 while Phil Salt made 25 off 19 balls.
Taskin dismissed opener Dawid Malan for five but Salt and Moeen Ali showed positive intent to put on 34 runs for the second wicket.
The visitors then lost Salt, skipper Jos Buttler (four) and Ali (15) in consecutive overs to ruin their prospect of putting in a big total.
Mehidy then struck twice in one over to dismiss Sam Curran (12) and Chris Woakes (0) to deny England a late recovery.
Bangladesh in their reply lost both their openers Liton Das (nine) and Rony Talukdar (nine) cheaply but young Towhid Hridoy made 17 to steady the innings.
Najmul and Mehidy put Bangladesh in charge with a 41-run stand. England sniffed a chance with a few late wickets as Jofra Archer wracked havoc to finish with 3-13.
However, Najmul thwarted the visiting side with his unbeaten 47-ball innings featuring three boundaries.
Taskin completed the win with consecutive fours off Chris Jordan in the 19th over.
The third and final match of the series will be held at the same ground on Tuesday.
England won the preceding three-match one-day international series 2-1.
The matches are important practice for England on South Asian pitches ahead of the ODI World Cup to be held in India later this year.
