Uruguay remain in fifth place in the South American group with 19 points and three matches to go, seven points behind leaders Argentina and Colombia.
The top four at the end of the campaign will go through to the finals with the fifth-placed team going into a play-off with an Asian qualifier for another berth.
Uruguay went ahead with a penalty in the 42nd minute when Suarez went down under a challenge from behind by Christian Ramos although it was far from clear from video replays whether the Peru defender had touched the striker.
Peru's players complained bitterly before Suarez calmly hit his spot kick low into the corner to his left with Raul Fernandez diving the other way.
Just before the halftime whistle, Yoshimar Yotun was sent off after kneeing Suarez in the back then trying to force the striker to get up believing he was feigning injury.
Play was end-to-end in the second half as Peru's 10 men tried to get back into the match while Uruguay sought to put it beyond their reach with fast counter-attacks.
Uruguay struck again in the 67th minute when a defender cleared from the feet of substitute Christian Stuani only for the ball to roll to Suarez who drove it into the roof of the net for his 10th goal of the qualifiers.
Peru winger Jefferson Farfan pulled one back six minutes from time by putting a fine free kick out of reach of goalkeeper Fernando Muslera.
Striker Claudio Pizarro was twice denied by good saves from Muslera in the first half.