Timothy Weah put the Stars and Stripes ahead just after the ten-minute mark, but there was nothing Steffen could do to prevent the hosts from equalising soon after.
West Ham’s Michail Antonio picked up play just inside the US half before cutting in on his right foot and unleashing an unstoppable 30-yard drive past the despairing dive of the City man and into the top corner to haul the Reggae Boyz level.
Jamaica went close again soon after the restart when a miscued DeAndre Yedlin clearance found an unmarked Bobby Reid inside the six-yard box, but Steffen was quick off his line to put the Fulham forward off as he skied his effort.
The hosts did eventually have the ball in the net once again with five to play, but Damion Lowe was judged to have fouled Walker Zimmerman as he rose to head home the corner.
Canada’s 2-1 victory over third-placed Mexico means the US drop to second in CONCACAF World Cup qualifying, one point off top spot.
It's shaping up to be a four-horse race as qualification edges over the halfway mark, with only two points separating the table-topping Canadians and fourth-placed Panama, who occupy the play-off spot.
City’s Brazilian duo, Ederson and Gabriel Jesus, had already guaranteed their place in Qatar thanks to a 1-0 win over Colombia last time out before facing Argentina in a rerun of this summer’s Copa America final.
It means Brazil’s six-point cushion at the top of South American qualifying remains, but the stalemate was enough to guarantee Argentina’s place at the 2022 World Cup.