The Americans looked to be in complete control after midfielder Michael Bradley then striker Chris Wondolwski scored in the first half but they wilted in the second term.
The US thought they had regained the lead when substitute forward Eddie Johnson scored with five minutes to go but the goal was disallowed for offside, although television replays suggested his strike should have counted.
"It looked good to me," Bradley told ESPN. "But sometimes these things work for you and sometimes they work against you.
"From a big picture point of view, we're happy. There were a lot of positives."
Bradley opened the scoring in the 15th minute when he half-volleyed a cross from Graham Zusi into the net from the back post.
Then he set up his team's second goal when he headed the ball towards Wondolwski, who poked it in from close range to double the American team's lead in the 28th minute.
The Mexicans, who arrived late to the University of Phoenix Stadium after getting stuck in heavy traffic, found their rhythm in the second half.
An unmarked Marquez headed home a corner from Marco Fabian four minutes after the restart then Pulido calmly tapped in a rebound after Paul Aguilar's angled shot hit the post in the 67th minute.
"Giving away an early goal (in the second half) doesn't help," said Bradley. "But all in all, I think it was still a good night and we're looking forward to the World Cup."
The Americans are due to play three more friendlies before they head to Brazil in June while Mexico, who have also qualified for the World Cup, have four more practice matches scheduled.
At the June 12-July 13 finals, the US are in Group G with Germany, Portugal and Ghana, while Mexico are in Group A alongside hosts Brazil, Croatia and Cameroon.
- Sports & Recreation
- Michael Bradley
- Rafael Marquez
- Alan Pulido