Russell hit 47 off 21 deliveries with six sixes and one four to keep the hosts in the hunt as they chased Bangladesh’s total of 184-5 in Lauderhill, USA.
However his fall in the 18th over – to left-arm seamer Mustafizur Rahman (3-31) – sealed the match for Bangladesh.
Russell’s exit at 135-7 after 17.1 overs was followed by rain which ended play.
Bangladesh lost the Test series 2-0 but bounced back in the limited-overs leg, with the 2-1 T20 series win following a similar result in the ODIs.
The big total was set up by Liton Das who hit 61 off just 32 balls with six fours and three sixes. The Tigers’ total was also boosted by Tamim Iqbal who helped add 61 off just 4.4 overs with Das for the opening wicket.
“This was a tremendous team effort and will give us a lot of confidence moving forward,” said captain Shakib Al Hasan. “Now we need to build on this performance, in both the ODI’s and T20’s, when we return home to be more consistent and competitive against the big teams.”
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