The referee issued a red card to Sebastian Saucedo for a studs-up challenge on Mauro Rosales in the 76th minute. The MLS-leading Whitecaps quickly capitalized when Mattocks headed home Russell Teibert's left-footed cross 4 minutes later.
It was the first goal conceded by Real Salt Lake in 262 minutes.
In other matches, Seattle beat Colorado for the fifth straight time 3-1, Los Angeles rallied to defeat Sporting Kansas City 2-1, and Fabian Castillo scored the fastest goal in FC Dallas history to help beat Toronto FC 3-2.
Neagle bent in his first goal of the season from the corner of the penalty area in the 5th minute. Colorado equalized in the 22nd, but Neagle put Seattle back on top two minutes later when he tapped in the rebound of his own attempt.
Martins used a beautiful individual effort in the 73rd minute to score his fourth goal of the year. After a Colorado turnover near midfield, Andy Rose sent a long ball over the top of the Colorado defense. Martins' back-heel first-touch split two defenders and he chipped the ball past goalkeeper Clint Irwin.
Omar Gonzalez scored in stoppage time as Los Angeles won its second straight game.
Gonzalez redirected Juninho's corner kick with his right shin in the fourth minute of extra time and it deflected off a defender's knee into the back of the net.
The Galaxy's Baggio Husidic opened the scoring in the ninth minute.
Castillo scored twice for FC Dallas, including a goal 29 seconds into the match that set a new record for the fastest in club history.
The goal came when he beat the back-line defense to Moises Hernandez's long ball and scored on a right-footed toe punch. He added his second in the 10th minute and Blas Perez made it 3-0 in the 27th.
Sebastian Giovinco got two goals back in the 83rd and 89th minutes, but Toronto lost its fourth in a row since winning its season opener.
Elsewhere, Ricardo Clark got the equalizer for Houston in the 65th minute in a 1-1 draw against D.C. United.
Chris Rolfe opened the scoring in the 36th for United, which moved into a tie atop the Eastern Conference table with the New York Red Bulls.