But Michael Bradley slipped the ball inside the area to Evans who, with a surprising amount of space, drove past Jamaican keeper Donovan Ricketts to seal the win.
The victory moves the United States to seven points from four games as they bid to earn one of three automatic qualification spots from the six-team CONCACAF final qualifying group.
Juergen Klinsmann's team went close to an opener in the second minute when Bradley struck the post with a drive from 20 yards out.
The United States took the lead when Altidore, who had an early effort ruled out for offside, rose to power in a superb cross from winger Graham Zusi.
Nine minutes later Jamaica almost drew level when Rodolph Austin burst through on to a Ryan Johnson pass but his low shot struck the post.
The United States looked in charge but with a minute of normal time remaining Beckford was left unmarked to head home from an Austin cross.
However, there was more drama to come and three minutes later the United States restored their advantage to get their first away win in qualifying.
The United States host Panama in Seattle on Tuesday and finish their trio of June qualifiers against Honduras in Salt Lake on June 18.
- Sports & Recreation
- Jozy Altidore
- Michael Bradley