Clint Dempsey put the US ahead with a goal in the 40th minute before Pappa fired the equaliser under the cross bar before goalkeeper Tim Howard had a chance to react.
It was a disappointing result for the Americans who were expected to win the Central and North American region (CONCACAF) third round match but instead squandered a chance to take control of Group A.
The US opened the campaign with a 3-1 win over Antigua and Barbuda and have four points to leave them level with Jamaica, who drew 0-0 with Antigua and Barbuda on Tuesday.
Aiming to reach their first World Cup finals since 1986, Canada spurned several golden opportunities to score in front of their home fans in Toronto, with Kevin McKenna's header coming closest to breaking the deadlock.
Midfielder Atiba Hutchinson was at the heart of Canada's attacking play in a physical first half that saw five yellow cards dished out.
Canada, who edged Cuba last week, have four points from two matches in Group C, while Honduras earned their first point.
Panama beat Cuba 1-0 in the day's other match to move into second place on three points.
Goals have been hard to come by for the Canadians, including a scoreless draw against the United States in a warm up international before the recent raft of qualifiers, and the issue remained a problem against the Hondurans.
Dwayne De Rosario was unable to convert any of his three first half attempts on goal as Hutchison, starting despite concerns over a long-standing knee injury, also forced a smart save from goalkeeper Noel Valladares in the second half.
Canada return to action September with home and away matches against Panama before concluding the third round campaign at home to Cuba and away in Honduras, who qualified for the 2010 World Cup in South Africa, a month later.
The top two finishers from the three groups advance to a final six-team pool offering three automatic berths for the finals in Brazil. The fourth-placed side will meet the OFC region winners in a two-legged play-off for a 2014 spot.