The team reached the target of 35 runs in the fourth innings within 10 overs on the fourth day. Amite Hasan almost took the Tigers to a win, but was stumped just before the end of play.
Shamim Hossain ended the match not out at 20 runs while Parvez Hossain Emon wrapped up the match with six.
England began Sunday at Zahur Ahmed Chowdhury Stadium in Chattogram in trouble, with their second innings standing at 89-6 wickets, but seemed to recover thanks to George Hill and Luke Hollman who scored 45 for the seventh wicket stand.
Spinner Minhazur Rahman gave the Tigers the breakthrough, catching Hill (32) before the stumps. The remainder of the team collapsed under Minhazur, who picked up the final three wickets as well.
Rakibul Hasan, another left handed spinner, holds the record after bagging 7 wickets for 93 runs against Sri Lanka last October.
The second and final youth test is to be held in the same venue on next Friday.
Brief scores:
England Under-19 1st Innings: 280
Bangladesh Under-19 1st Innings: 398/9
England Under-19 2nd Innings: (Previous day 89/6) 152 in 84.3 (Hill 32, Hollman 29, Qadri 5, Finch 4, Morley 0*; Galib 3/30, Shamim 0/7, Ruhel 0/8, Minhazur 6/28, Rakibul 0/ 48, Hridoy 0/11, Shahadat junior 1/6)
Bangladesh Under-19 2nd Innings: (Goal 35) 40/2 in 10 overs (Tanzid 0, Amite 10, Shamim 20*, Parvez 6*; Finch 1/6, Hollman 1/19, Qadri 0/11)
Result: Bangladesh Under-19 won with 8 wickets
Man of the Match: Minhazur Rahman