After suffering a 4-0 defeat at home to Spain in a friendly on Saturday, US coach Bob Bradley reverted to his tried and tested formula and it delivered the kind of solid display his team have become noted for.
German-born Jermaine Jones and Bradley's son Michael were impressive in the centre of midfield while in attack Altidore, who continues to under-achieve at club level, delivered a much-needed reminder of his qualities.
Canada still have a chance to progress from Group C, which also features Panama and Guadeloupe, but were disappointing until the final stages when they finally tested U.S. keeper Tim Howard and his defense.
"We were predictable and moved the ball too slowly at times," said Canada head coach Stephen Hart.
"Too many players didn't want the responsibility of the ball but if we play like we did in the second half we will get results."
A crowd of 28,000 at the Detroit Lions' NFL stadium Ford [ Images ] Field saw the United States make a strong, determined start.
Altidore opened the scoring in the 15th minute with a smart shot on the turn that crept under the body of Canadian keeper Lars Hirschfeld, who will be disappointed he did not keep the ball out.
With Jones and Bradley taking charge, the United States were comfortably on top without creating many real chances.
The Americans extended their advantage in the 62nd minute when Altidore turned provider, bursting down the right flank and delivering a firm, low cross to the back post where Dempsey slid the ball in.
Canada finally came alive with substitute striker Ali Gerba twice bringing great saves out of U.S. keeper Howard, who had little to do in the opening 70 minutes.
Gerba broke free down right and struck a fierce shot which was expertly tipped over by Howard. Then the Everton keeper made a double save in the 85th -- first bravely at the feet of Joshua Simpson and then rising to parry another Gerba shot.
"I didn't think we did a good enough job of closing the game out, it is essential that improves," said coach Bradley.
The return to form of Altidore, who had not scored in a competitive international since September 2009 and managed just one strike all season with his Turkish club Bursaspor, was the biggest positive for Bradley.
"For confidence it was a good game for Jozy ... when you go through a stretch with your club team, not playing many games and not scoring goals, in terms of confidence this was very important".
Panama hold on to beat ten man Guadeloupe
Panama survived a late comeback from 10-man Guadeloupe before holding on for a 3-2 victory in their CONCACAF Gold Cup Group C opener on Tuesday.
After leading 3-0 inside the hour, the Central Americans looked to have the game in the bag, especially with a man advantage following the sending off of Guadeloupe's Michael Tacalfred.
But Guadeloupe, who many would expect to finish bottom of a group that also features the United States and Canada, showed plenty of character and attacking ability to give Panama a scare.
"We should not have had so many problems at the end after we had that game under control," said Panama head coach Julio Cesar [ Images ] Dely Valdes.
"We suffered at the end having been on top throughout the game, thankfully we gave ourselves a three goal cushion".
Blas Perez put Panama ahead in the 29th minute, pouncing inside the area and firing home on the turn, then two minutes later, a fine solo effort from Luis Tejada doubled the advantage.
Things got even trickier for Guadeloupe after they had Tacalfred sent off in the 38th minute for a foul on Luis Henriquez.
A twice-taken Gabriel Gomez penalty, after the impressive Perez was brought down, looked to have put the game beyond Guadeloupe.
But the team from the French-controlled territory showed real character with two late goals from Brice Jovial.
In the 64th minute the powerful striker bustled into the area, shrugging off two challenges and driving home to make it 3-1. Then, after 15 minutes of pressure, Richard Socrier produced a great turn and low cross which Jovial slid in at the back post.
Panama have an injury worry over defender Adolfo Machado who was taken to hospital after being carried off 10 minutes from the end.