Defending 259 for seven at the Sher-e-Bangla Cricket Stadium, Pascal snatched four for 49 while Shillingford extended his good form with three for 38, to send the hosts tumbling to 230 all out off 46.5 overs.
The win was West Indies A’s second following their impressive 11-run victory over South Africa A in their opening match on Thursday.
Contrasting innings from left-handers Darren Bravo and Brendan Nash had formed the foundation of West Indies A’s innings after the visitors won the toss and opted to bat.
While the stylish Bravo crafted a patient 69 from 114 balls, the usually workmanlike Nash clobbered an uncharacteristically explosive 60 from 46 balls.
Bangladesh then seemed poised to overhaul their total with some ease when they reached 176 for three in the 35th over. However, Pascal and Shillingford accounted for six of the next seven wickets which tumbled for 54 runs as the young Tigers folded meekly.
Seamer Lionel Baker got West Indies A off to a fine start when he removed opener Uttam Sarkar caught and bowled without scoring, off the fifth ball of the innings with Bangladesh yet to score.
Opener Nazimuddin, who stroked 89 from 86 balls with 13 fours, then rebuilt the innings in an 84-run, second wicket partnership with captain Shamsur Rahman who scored 23 from 33 balls.
When Shillingford removed Shamsur to a catch at the wicket by Chadwick Walton, Rokibul Hassan joined Nazimuddin to add another 63 for the third wicket and keep Bangladesh on course for victory.
Rokibul hit 46 from 60 balls with two fours and took the lead role in the partnership before leg-spinner Imran Khan struck a big blow by removing Nazimuddin with the score on 147 for three in the 29th over.
Bangladesh were getting on top again through a 29-run fourth wicket stand between Rokibul and Marshall Ayub (43) when Imran Khan struck again, trapping Rokibul lbw.
It was the breakthrough West Indies A needed. Pascal returned with an incisive spell to capture the next four wicket to fall as Bangladesh A plunged to 224 for eight, and Shillingford wrapped up the tail with wickets in successive deliveries in the 47th over.
Earlier, West Indies slumped to 27 for two in the fifth over before being revived by three great partnerships.
Captain Travis Dowlin, who scored 37 from 64 balls, shared 84 for the third wicket with Bravo who counted seven fours in his knock before Nash and Bravo posted another 53 for the fourth wicket.
Nash, known more for his ability to graft, was in cracking form as he smashed three fours and three sixes.
When he lost Bravo at 164 for four in the 39th over and Kirk Edwards for 12 just five overs later, he blasted a quick-fire 42 off 24 balls for the sixth wicket with Imran Khan whose 31 came from 27 balls.