The Whitecaps had the first chance of the match but Tim Melia made a fine save to keep the scores level by denying Octavio Rivero's header from close range after the forward latched on to Mauro Rosales's cross.
Nemeth almost doubled his side's advantage when he saw his strike clatter off the post, while Jacob Peterson put his effort from the rebound wide.
Vancouver responded and only a goalline clearance from Amadou Dia kept Sporting in the lead as Techera's strike deflected off Melia and Matt Besler and almost found its way in before the defender smashed the ball clear.
Peterson almost notched a second for Kansas City when he fired low at goal, but Ousted made the stop, while at the other end Melia made another fine save to tip Rivero's free kick over the bar.
The Whitecaps pushed for an equaliser in the dying minutes, but Melia was once again in fine form as he made an impressive diving stop to tip away Parker's effort and secure the win for his side.