Chasing 145 to win, Bangladesh were well-placed at 78-2 before losing their last eight wickets for 60 runs to crash to defeat two days after losing the opening match by five wickets.
Fast bowler Ali Khan claimed 3-25 for the home side while Bangladesh skipper Najmul Hossain Shanto (36) and former captain Shakib Al Hasan (30) were their team's main run-makers in a total of 138.
The series is being played as part of the build-up to the Twenty20 World Cup in the United States and Caribbean which starts on June 1.
After limiting the USA to 144-6 in 20 overs, Bangladesh were rocked after just four balls when opener Soumya Sarkar was caught and bowled by Saurabh Netravalkar without scoring. They were 30-2 in the fifth over when fellow opener Tanzid Hasan, who had been called into the side to replace veteran run-getter Liton Das, was clean bowled by Jasdeep Singh for 19.
At 78-2, Bangladesh appeared in control but lost skipper Shanto, run out an embarrassing mix-up with Towhid Hridoy. His exit sparked a rapid slide by the Asian side who are ranked at nine in the world compared to the Americans at 19.
Hridoy was bowled by former New Zealand star Corey Anderson for 25 before 38-year-old Mahmudullah (three), the veteran of 130 T20s, was also cleaned-up by left-arm seamer Shadley van Schalkwyk. The same bowler also sent back Jaker Ali and when Shakib, playing in his 121st T20 international, had his stumps scattered by Khan, the Bangladeshis were 124-7 and staring at defeat.
Tanzim Hasan Sakib was lbw to Khan, Shoriful Islam fell to Netravalkar before Khan had last man Rishad Hossain caught behind to end the match. Earlier, US skipper Monank Patel top-scored with 42 off 38 balls and was well-supported by fellow opener Steven Taylor (31) and Aaron Jones's 35.
Shoriful, Mustafizur Rahman and Rishad all took two wickets each for Bangladesh.
The final game also takes place in Houston on Saturday.