The former US Open champion from Portrush picked up three birdies on the front nine to move into contention.
But his challenge faded with dropped shots at the 14th, 17th and 18th leaving him with a level-par 72.
McDowell finished on four under for the tournament and six shots behind winner Brian Harman.
Harman made a 28-foot birdie putt to win and end Dustin Johnson's hopes of winning a fourth title in his last four starts.
World number one Johnson, on his return from injury, shot a five-under 67 to set the clubhouse lead on nine under.
Ireland's Shane Lowry (72) ended on three under with Seamus Power (73) back on one over.

The Antonov An-12 plane, which was heading to a factory in Irkutsk, caused a fire at the military unit, but there were no casualties on the ground.
Six crew members and three others on board were killed.
The authorities have given no explanation for the crash, but Russia has a poor air-safety record.
Accidents are relatively frequent and planes are often poorly maintained, according to safety experts.

Mr Hands said officials would be able to choose the type of products to be covered by agreements.
The union operates alongside the EU's single market and free trade area.
It comes after the Brexit secretary said the UK would consider paying for "best possible" single market access.
The customs union includes all 28 EU nations, but also Turkey, Monaco, San Marino, Andorra and non-EU UK territories such as the Channel Islands.
They enjoy free trade with each other, but must impose the same tariffs on goods from nations outside the pact and are barred from doing bilateral trade deals with other countries.
Bloomberg news agency published remarks Mr Hands made in an interview this week in which he said the "history of international trade has got all kinds of examples of customs unions".
He said the UK could be selective about which individual sectors it wished to be covered by any customs union arrangement.
Mr Hands added: "You can choose which markets, which products the customs unions affect and which they don't, so there isn't a binary thing of being inside the customs union or outside of the customs union."
As the pound posted its fifth consecutive week of gains against the euro, Mr Hands's words were cited by financial market commentators as further evidence that fears over a "hard Brexit" were easing.
In the Commons on Thursday, Brexit Secretary David Davis had said the "major criterion" was getting the best access for goods and services to the European market.
Later, in a speech to CBI Wales in Cardiff, Mr Davis sought to reassure business leaders that immigration controls after Brexit will not be imposed "in a way that it is contrary to the national and economic interest".
But Brexit-backing Tory MP Peter Bone said "people would be absolutely outraged" if the UK continued to pay the EU after Brexit.
And another prominent Leave campaigner and former Conservative cabinet minister, Iain Duncan Smith, told the BBC he believed Mr Davis had been simply not ruling anything in or out of the government's Brexit negotiations.

The wall, which was nine feet high, was sent crashing down in Listmas Road, Chatham, just before 22:00 GMT.
Equipment normally used to find casualties buried under collapsed buildings was drafted in to help specialists assess the damage.
A fire service spokesman said no-one was injured, adding that the cause of the collapse was unknown.
Graeme McDowell carded three late bogeys to finish in a tie for 18th at the Wells Fargo Championship in North Carolina on Sunday.
[NEXT_CONCEPT]
A Russian cargo plane has crashed into warehouses at a military facility in Siberia, killing all nine people on board, officials have said.
[NEXT_CONCEPT]
The UK could seek a deal which would allow sections of the economy to remain within the EU's customs union after Brexit, international trade minister Greg Hands has suggested.
[NEXT_CONCEPT]
A 130ft long wall suddenly collapsed on to a Kent road severely damaging a number of vehicles on Thursday night.