McDowell, who was risen to 55th in the world rankings, finished with a one-under-par 69 to finish five strokes behind winner Adam Scott.
The Portrush player had started the day at three under, after an impressive 67 on Saturday.
It qualifies the 36-year-old for the WGC-Cadillac Championship which starts at Trump Doral on Thursday.
McDowell started his round with a birdie three on the first, and then bogeyed the fifth and birdied the eighth to reach the turn in one-under 34.
A dropped shot on 12 was recovered with birdie on the 13th to move into a top-five position.
Defending champion Padraig Harrington finished 43rd in the West Palm Beach tournament after a closing 71 put him on four-over-par 284.

Glenn Murray put the Eagles ahead when he headed in from close range after Bolasie's deflected cross.
Bolasie added a second soon afterwards as he poked the ball past Costel Pantilimon after Murray's knockdown.
A lofted finish from Bolasie made it 3-0 and he completed his treble from Murray's pass before Connor Wickham volleyed in a late consolation.
The result, the second time in three home games that Sunderland have conceded four goals, increases the Black Cats' relegation fears.
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They have been in the Premier League for eight successive seasons but are now 16th in the table, only three points above QPR and Burnley.
Sunderland have only six games left to save themselves, but their last two matches of the season are away at Arsenal and then at current leaders Chelsea.
Dick Advocaat, brought in after former manager Gus Poyet had been sacked following a 4-0 home defeat by Aston Villa, had stressed the importance of this match to his side.
But he was let down by some woeful defending as the hosts capitulated and conceded four goals in a 14-minute spell early in the second half.
After a quiet first half that was low on quality and goalscoring chances, but high on fierce challenges, the match sprung into life within three minutes of the restart.
Murray headed in his sixth goal in six games to set Palace on their way to their eighth win in 12 Premier League games since Alan Pardew took over at the start of the January.
But even he could not have expected what was to follow.
The hosts fell apart and three minutes later Bolasie, with one goal in his previous 27 league matches this season, got to Murray's flick-on first to make it 2-0.
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The third goal was a poor one to concede, although Bolasie showed great technique to lift the ball over advancing Sunderland goalkeeper Pantilimon.
Sunderland, who had beaten Newcastle 1-0 in their last match, fell further behind as Murray again linked up with Bolasie and he scored at the second attempt after being initially denied by Pantilimon.
Advocaat had named what looked an attacking line-up with Jermain Defoe, Steven Fletcher and Wickham named in a three-man forward-line, although it took the hosts 44 minutes to record a shot on target.
In front of a near-empty home support, who left the ground en masse after Palace's fourth goal, Wickham did well to steer the ball into the net in the 90th minute after Patrick van Aanholt's pullback.
But it could not take the shine off Palace's day as they boosted their hopes of finishing in the top half of the Premier League for the first time ever.
However, for Sunderland it was another dark day at the Stadium of Light.
Sunderland boss Dick Advocaat said:
"We have to recover in 14 days with an away game against Stoke and we have to do better as this was not good enough.
"After the Newcastle game we did not see this performance coming. We had trained really well and the confidence had come back. We gave the match away in the first 10 minutes of the second half.
"We could not cope with their pace, but I don't want to complain about the players. We win as a team and lose as a team.
"We still have six matches left and it's in our hands. You cannot lose 4-1 to Crystal Palace in a home game because we need to get results."
Northern Ireland's Graeme McDowell has been buoyed by finishing fifth at the Honda Classic in Florida.
[NEXT_CONCEPT]
Yannick Bolasie's 11-minute hat-trick helped Crystal Palace humiliate relegation-threatened Sunderland.