Asalanka smashed an unbeaten 49-ball 80 while pairing in two half-century stands, adding 69 with Pathum Nissanka (24) before stitching up a match-winning 86 with Rajapaksa (53) for the fifth wicket at Sharjah on Sunday.
Bangladeshi fans had their hearts in their throat when Liton Das fluffled Rajapaksa on 8 off Afif Hossain and Asalanka on 63 of Mustafizur Rahman two overs later in two crucial lapses which allowed the Islanders to steer to the win with 7 balls remaining.
Having posted a challenging total, Bangladesh began their defence well when Nasum Ahmed went through the gates of Kusal Perera (1) in the opening over.
Asalanka then put up resistance with Nissanka as the duo cracked regular boundaries to keep up with the required rate, bludgeoning 54 runs in the powerplay.
With the duo easing through on 1 for 71 in the ninth over, Mahmudullah brought on Shakib Al Hasan who snuck through the gates of Nissanka and Avishka Fernando (0) in the space of four balls, becoming the highest wicket-taker in T20 World Cups with 41, leaving Shahid Afridi (39) behind in second place.
Six balls later, seamer Saifuddin bagged Wanindu Hasaranga de Silva (6) scalp to leave Sri Lanka stuttering on 79 for 4 as the Tigers roared back into the game.
The bowling from the men in red and green, however, was not on point as wayward deliveries were duly punished by Asalanka and birthday boy Rajapaksa.
Bringing Afif on for a change, Mahmudullah expected to reap a surprising reward. Although the offspinner was clubbed for six in his first ball, he came up with the opportunity when Rajapaksa skied a sweep but Liton ran it only to grass it at square leg.
It was a similar blunder off Mustafizur two overs later but this time in extra cover and all Bangladeshi hands were on heads.
The batsmen took full advantage by hammering Saifuddin for 22 in the following over. Nasum did pick out Rajapaksa after he reached his fifty off 28 deliveries, but it was all too late by then.
Earlier, gritty fifties from opener Naim Sheikh and Mushfiqur Rahim have hoisted Bangladesh to a challenging 171 for four.
Asked to bat, the Tigers were off to a breezy start and found their footing with the bat after qualifying in second place of Group B in the qualifiers.
Naim (62 off 52 balls) and Liton Das (16) forged a solid 40-run opening stand. Mushfiqur then joined in and paired up with Naim for a fluent 73 in the third wicket.
Naim cracked six boundaries for his fourth T20I half-century before falling as Binura Fernando’s lone wicket, but Bangladesh were all set up for a late burst.
Mushfiqur pressed on, sweeping and cutting away to a blistering 37-ball knock, including five boundaries and two sixes in his sixth T20I half-century.
The little man, who has been quiet with the bat as of late, helped Bangladesh collect 53 runs in the last five overs.
For Sri Lanka, all bowlers struggled to make a dent to the pace of the Tigers’ innings.
Chamika Karunaratne (1-12), Fernando (1-27) and Lahiru Kumara (1-29) bagged Bangladeshi wickets while Afif Hossain (7) ran himself out.
After the match, Dasun Shanaka said, “It was not the easiest target to chase but once batsmen are set, any target can be chased. It was an outstanding innings from Asalanka. It's very important that youngsters step up at this stage, it was really nice to see that.”
Mahmudullah said at the post-match presentation: “I thought 171 could be defended. Liton and Naim gave us a very good start. Naim held the innings. Mushfiq played a brilliant innings. We were in the game till the tenth over. But things went wrong for us after that.
“We will correct that in the next game. We watched the IPL games and thought an extra spinner would help. The spinners bowled well but we missed a couple of chances.
This game will boost up our batting unit and we are looking forward to the next game.”
The Tigers will take on England in their next Group 1 tie of the Super 12 on Oct 27 in Abu Dhabi.