A poor finish from Luis Solignac, who sent a decent chance high over the crossbar, kept proceedings level at Sporting Park before the break, and the home side failed to strike in a first half for the ninth league game in a row.
The Rapids were able to take advantage of their opponents' attacking approach by hitting them on the counter, and in the closing stages of the match, Doyle and Powers caught Kevin Ellis and Mustivar out of position.
Doyle laid the ball off to Powers, who chipped over the goalkeeper and found the back of the net to put the visitors 1-0 up with just 13 minutes of normal time remaining.
Sporting KC almost equalised in the 82nd minute when Jordi Quintilla came close, but his effort flew just wide of the target, and two minutes later the hosts were dealt a double blow when Sam Cronin was sent off for a second yellow.
The Rapids took advantage again on the break as Sarvas grabbed his side's second to leave Sporting KC fifth in the Western Conference, while the visitors reside bottom of the table.