Tottenham striker Dempsey broke a 1-1 deadlock with a goal in the 18th minute and added another in the 36th minute to spark the Americans, while the Guatemalans were eliminated when Jamaica beat Antigua and Barbuda 4-1.
"Credit my team-mates. They were putting good balls in. I was lucky enough to get them to go in," Dempsey said. "A little pressure on us but it's behind us now. We want to go to the World Cup. This is the first step to getting there.
"We haven't been able to get too many wins away from home," Dempsey said. "If we start getting wins away from home and keep our results at home, I think we'll be all right."
Carlos Ruiz gave Guatemala the lead with a goal in the fifth minute to put a scare into the Americans at Kansas City. US captain Carlos Bocanegra answered in the tenth minute to equalise, setting the stage for Dempsey's double strike.
At Kingston, Jamaica's Reggae Boyz advanced thanks to goals by Dane Richards in the 78th and 88th minutes. Jamaica and Guatemala each finished 3-2 with one drawn in Group A but Jamaica moved on due to superior goal difference.
Quinton Griffith pulled one back for visiting Antigua and Barbuda in the 61st minute, putting Jamaica's FIFA World Cup dream at risk before Richards saved the day.