De Rosario beat goalkeeper Franck Grandel in the 51st minute after Stephane Zubar was given a yellow card for bringing down Ali Gerba in the penalty area.
''I was very fortunate to put the penalty shot in and create a victory for us,'' De Rosario said.
Jean-Luc Lambourde put Guadeloupe at a disadvantage during the fourth minute when he received a red card following a lunging tackle on Canada's Will Johnson.
''We didn't want to change what we set out to do ... just be patient,'' Canada coach Stephen Hart said. ''It was very, very hot. Make them run. Keep the ball moving and just be careful not to get caught on the counter-attack.''
An offside call negated a goal by Gerba 15 minutes into the first half. Gerba had a shot go just wide at the 33-minute mark.
Thery Racon had a good scoring chance during the opening minute of the second half, but was stopped by Canada goalkeeper Milan Borjan.
''They created some pretty good goal-scoring opportunities,'' De Rosario said. ''At the start of the second half, we started flat and they almost scored a goal. The main thing was we didn't lose our heads in the game. We didn't let them get us a red card.''
Grandel kept the Guadeloupe deficit at one goal with a strong save on Simeon Jackson in the 65th minute.
''We played very well with 10 men,'' Guadeloupe coach Roger Salnot said through a translator. ''We did everything we had to. Just didn't get a result at the end.''
Canada was coming off a 2-0 loss to the United States in its opening game last Tuesday. Canada had not scored a Gold Cup goal in its previous 242 minutes entering Saturday's match.
Brice Jovial scored twice as Gaudeloupe dropped a 3-2 decision against Panama in its first game on Tuesday. Michael Tacalfred was shown a red card in the first half of that match for a foul on Luis Henriquez.
In its only two previous trips to the Gold Cup, Guadeloupe reached the semifinals in 2007 and appeared in the quarter-final two years ago.
Winless Guadeloupe will face the U.S. in its final group match on Tuesday.
''We will play to the end,'' Salnot said. We will still play to win. Leave this game behind.''
Canada will face Panama on Tuesday.