Najmul batted from the fourth over to the 13th, and captain Shakib Al Hasan completed the victory with the winning boundary through deep backward point in an unbeaten 34 off 24.
Bangladesh reached 158-4 after England was restricted to 156-6 in the first of three T20s.
The hosts made a brisk start to the chase. Rony Talukdar returned after eight years to play only his second game and made 21 off 14.
That brought in Najmul and he responded with four straight boundaries against fast bowler Mark Wood. Najmul brought up his third T20 fifty with a single off offspinner Moeen Ali and Wood returned to rattle his stumps.
“I was not too worried about losing wickets,” Najmul said.
Shakib took over steering the side on a slow pitch and managed it serenely in Bangladesh’s first T20 win over England. “The way we approached the game was fantastic; under the pump in the first 10 overs but no one panicked,” Shakib said.
Made to bat first, skipper Jos Buttler and Phil Salt gave England an ominous start. Buttler struck 67 off 42 with four fours and as many sixes while Salt hit 38.
They formed an 80-run partnership before left-arm spinner Nasum Ahmed made the breakthrough by removing Salt.
Buttler survived on 19 and was dismissed amid a collapse of four wickets for 12 runs. England took just 26 runs from the last powerplay.
“We were in a position to kick on but were 20 (runs) short,” Buttler said. “Low bounce and a little slow but (the pitch) stayed consistent throughout the game. Bangladesh took the game on and put us under pressure.”
Hasan Mahmud led with 2-26 from his four overs.
The second T20 is on Sunday in Dhaka.
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