The tourists' ploy of building up a big first innings total before trying to bowl out Bangladesh in two consecutive innings almost came off as they forced the follow-on on Thursday.
Michael Davies killed off the home side's first innings by clean bowling tailender Bikash Ranjan Das for two, before Paul Franks made an early breakthrough in the second by splattering the stumps of Shahriar Hossain for eight.
Shortly after that, Franks had Javed Omar caught behind off a brilliant delivery, then Chris Schofield sent Habibul Bashar back to the pavilion for just three. Bangladesh were reeling on 28 for three.
But the arrival of Mashud stopped England A's charge as he thrashed away for a sophisticated 105 not out, pairing up with Al Shahriar Rokon and captain Aminul Islam for the vital match-saving runs.
By the time the game ended, Bangladesh had progressed from dire circumstances on 142 runs behind and three men down to move into a 62-run lead. Rokon hit his second 50 of the match.
It was a valuable win for the home side, who were desperate to avoid the humiliation of an innings defeat. The overjoyed crowd lauded Mashud, but there was some controversy with England A convinced the player had been caught behind off Davies when he was on 81.
Scorecard
Bangladesh drew with England A
Overnight:
England A 356 (D J G Sales 63, V S Solanki 55, C P Schofield 54, A Habib 51;
Hasibul Hussain 5-85).
Bangladesh 186-9 (Al Shahriar Rokon 73; R J Kirtley 4-36).
Bangladesh First Innings
Hasibul Hussain not out 3
Bikash Ranjan Das b Davies 2
Extras lb8 w1 nb6 15
Total (71.2 overs) 186
Fall: 1-26 2-30 3-39 4-54 5-124 6-160 7-168 8-180 9-181
Bangladesh Second Innings
Shahriar Hossain b Franks 8
Javed Omar c Turner b Franks 1
Habibul Bashar c Turner b Schofield 3
Mashud not out 105
Al Shahriar Rokon b Davies 56
Aminul Islam not out 37
Extras b10 lb6 nb6 22
Total 4 wkts (86 overs) 232
Fall: 1-12 2-17 3-28 4-164
Did Not Bat: Mushfiqur Rahman, Enamul Hoque, Shabbir Khan, Hasibul Hussain, Bikash Ranjan Das.
Umpires: Syed Mahbub Ullah and Afther Uddin
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