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McIlroy ended up winning on 12 under par, two ahead of Woods, and Schwartzel moved up two spots with a closing 69 for a seven-under total 273 in the US PGA Tour event.
The Masters champion was five off the pace of the young Northern Irishman, but at the start of the round it was a familiar scene to the final round at Augusta last year.
Then, McIlroy enjoyed a four-stroke lead at the start of the last round before his famous collapse on the final nine, opening the door for Schwartzel to claim his maiden Major victory.
This time, both Schwartzel and McIlroy shot the same score as the Irishman went on to lift the title.
Schwartzel, meanwhile, moved back into the top 10 in the world rankings at ninth.
He is now just two places behind his career-high ranking of seventh, which he reached in May last year.
Schwartzel began the final round with a birdie on his first hole, before he picked up another stroke on the par-five third.
At that point it looked like Schwartzel was set for a surge up the leaderboard, but he played the next 15 holes in one over and was forced to settle in a tie for fifth.
The South African illustrated faultless ball striking during the tournament, but in the fourth round his putter went cold as he needed 33 putts for the 18 holes.
Conversely, McIlroy used the flat-stick just 28 times on Sunday.
Schwartzel's fellow South African, Ernie Els, did not fare much better with the putter.
Els had 32 putts, ending in a tie of 21st with a one-over 71 and a total of one under for the tournament.
The Big Easy averaged 297 yards off the tee, over 30 yards longer than Schwartzel.
Els also hit 10 greens, but his average distance to the hole per green in regulation was 52 feet, which did not help his cause.
The Big Easy would have had one eye on his world ranking, currently at 65, as he needs to get inside the top 50 if he is to qualify for the Masters in April.
If Els fails to make it into the field, it will be the first time he has missed the opening Major of the season since his maiden trip to Augusta in 1994.
Els has already said this year that making it into the Masters field is one of his early season goals, assisting to keep him motivated.
Rory Sabbatini rounded out the South African finishers with a tie for 62nd, falling 28 places on Sunday with a seven-over 77.
Louis Oosthuzien was forced to withdraw after nine holes, citing illness after he stumbled to an eight-over 43 for nine holes.
