Defending champion Schwartzel began the final round with a two-shot lead over playing partner Finch, but saw that wiped out in the space of three holes as the Englishman birdied the first and third.
Schwartzel responded with a superb tee shot to within a few feet of the hole on the fifth to edge back in front, but a birdie on the sixth was matched by Finch, playing here on a sponsor's invite after losing his card at the end of the 2013 season.
It looked as though Finch, who won twice on the European Tour in 2008, would get back on level terms after a brilliant second shot to the eighth, but Schwartzel holed from 20 feet and Finch did well to follow him in.
At 16 under par, 2011 Masters champion Schwartzel led by one from Finch, with Denmark's Soren Hansen a distant five shots adrift despite being two under par for his round.
English duo Simon Wakefield and Ross Fisher were another shot back alongside France's Romain Wattel.
Finch made his first mistake of the day on the 11th, a wild drive leading to a penalty drop and a bogey five, although Schwartzel almost let him off the hook.
From the middle of the fairway the South African span a simple wedge shot back into a greenside bunker and eventually had to hole from four feet for par to extend his lead to two shots.
Schwartzel moved three ahead with a birdie from 10 feet on the 13th and the tournament suddenly looked over as a contest when Finch ran up a double bogey on the next, his approach from a fairway bunker hitting rocks on the edge of a water hazard and bouncing into some bushes.
Schwartzel's birdie putt from six feet lipped out, but he still had a five-shot lead with four holes to play.