Delano Sam-Yorke gave the hosts a dream start, grabbing his fourth goal in three games with a powerful header which gave Sutton goalkeeper Will Puddy no chance.
Jamie Collins headed against a post as the visitors grew into the contest, before Kieron Cadogan equalised in bizarre circumstances when Terell Thomas' attempted clearance flew in off the Sutton winger.
But Ugwu then collected the rebound from his own initial shot to fire in the winner with seven minutes remaining to take Woking out of the National League relegation zone.
Match report supplied by the Press Association
Match ends, Woking 2, Sutton United 1.
Second Half ends, Woking 2, Sutton United 1.
Goal!  Woking 2, Sutton United 1. Gozie Ugwu (Woking).
Substitution, Woking. Jake Caprice replaces Joey Jones.
Substitution, Woking. Gozie Ugwu replaces Jamie Lucas.
Substitution, Woking. Connor Hall replaces Charlie Carter.
Goal!  Woking 1, Sutton United 1. Kieron Cadogan (Sutton United).
Nathan Ralph (Woking) is shown the yellow card.
Second Half begins Woking 1, Sutton United 0.
First Half ends, Woking 1, Sutton United 0.
Substitution, Sutton United. Gomis replaces Adam Coombes.
Ismail Yakubu (Woking) is shown the yellow card.
Ben Jefford (Sutton United) is shown the yellow card.
Goal!  Woking 1, Sutton United 0. Delano Sam-Yorke (Woking).
First Half begins.
Lineups are announced and players are warming up.
Gozie Ugwu's late strike secured Woking an important National League win over Sutton at Kingfield Stadium.