Uruguayan striker Rivero made it three goals in as many games for the Whitecaps, producing a diving header in the 96th minute at the Citrus Bowl to nod Pedro Morales' free-kick past Orlando goalkeeper Donovan Ricketts.
After losing their opening game of the season at home, Rivero's late header made it two straight road wins for Vancouver, who rose to second in the Western Conference standings with six points, three behind leaders Dallas.
Saturday's result means Orlando will have to wait at least another fortnight for their first win at home in MLS, after they came from behind to draw 1-1 against New York City on the opening weekend of the 2015 season.
The match against Vancouver was marred by a heavy collision between Ricketts and Whitecaps full-back Sam Adekugbe in the second half.
The two players crashed together as they both went to ground to challenge for a loose ball in Orlando's penalty area, with Ricketts' knees making contact with Adekugbe's chest.
Adekugbe was taken from the pitch on an ambulance-style stretcher but was cleared of broken ribs after the match.
It was a low-scoring day in MLS with just five goals across six matches, including three scoreless draws.
Dallas continued their perfect start to the season with a 2-0 win at Philadelphia Union in a match that had been rescheduled, after heavy snow forced a postponement on Friday.
Tesho Akindele and Ryan Hollingshead both scored in the second half for the Texan visitors.
Houston Dynamo came from behind to draw 1-1 away to Los Angeles Galaxy.
New England Revolution, Colorado Rapids and Sporting Kansas City were held 0-0 at home by Montreal Impact, New York City and Portland Timbers, respectively.
