Standing in for absent host Tiger Woods, McDowell needed to hole his second shot at Sherwood's 18th to tie with Furyk, who posted a final round 67 to set the 13 under par target.
The Ulsterman failed by six feet but certainly gave Furyk a fright as he rifled his approach at the flag and eventually tapped in for a closing birdie and a round of 70.
With world ranking points on offer for the first time, McDowell moved from 55th to 38th and can start booking his hotel accommodation in Augusta. (Rory McIlroy, incidentally, slipped out of the top 10 to 11th with Harrington remaining fifth.)
No wonder he wasn't too disappointed to step in for an under siege Woods at the last minute.
"It was such a bonus to get in here, and obviously the circumstances, we all know why," McDowell said. "You know, it was a bit of a blow for the event, but like I said, I feel very fortunate to be here, and to play as well as I have been playing.
"This year has been a funny year for me. I just feel like I started to play good the last few months, and I was running out of tournaments really, and it was nice to add another great tournament like this on the schedule and to play as well as I did, very satisfying. And the boost up the world rankings is obviously just huge for me really.
"It's been a frustrating year. I've got nothing out of all the work I've put in, and in a funny way this kind of puts a bit of a shine on it and gives me a little something back for all my hard work this year."
McDowell and US PGA champion YE Yang led by a stroke from Padraig Harrington and Lee Westwood with Furyk and Ian Poulter a further shot back.
Harrington was at his erratic best or worst, chipping in three times in his round- twice for eagle. The last of those yielded an eagle three on the 16th that left him just two off the pace. But he could only par the short 17th and had to birdie the last for a 70 to secure third place alongside Westwood, who came to the last needing a birdie to tie.
"You know, I had seven three-putts," Harrington said, assessing his week. "I hit a number of other putts, and not that I hit bad putts. I just kept hitting them -- for some reason I kept hitting my right-to-left putts high, and I was seeing a right-to-left break that wasn't there. So obviously I could have done better today. A couple of error in shots, but it just wasn't my week in that sense. I can't give up that many on the greens."
As for his season, Harrington explained: "It was a disappointing season in terms of results, but a very positive season in terms of the benefits. So I'm happy, I'm happy going forward. That's it. It's probably a good year to put behind me, too."
Bunkered off the tee, Furyk holed a long putt down the 17th green for par to remain at 12 under before European No 1 Westwood drew level when he birdied the penultimate hole from six feet.
But as Furyk birdied the last with a brilliant 7-iron to six feet, Westwood was left needing to hole a 30 foot birdie putt from the fringe to force a play-off.
After a lengthy debate with a rules official over a sprinkler head that impeded his stance, the English start got a favourable drop on the fringe but three-putted for a bogey and a round of 70 that relegated him into a tie for third with Harrington on 11 under par.
That hardly mattered to Furyk, who ended his 29-month title drought with a typically workmanlike performance.
"It has bothered me that I haven't won, I would be lying to say otherwise," Furyk said. "That's your goal every year and when it doesn't happen it definitely bothers you.
"Honestly, this week was a stepping stone. Get one under your belt and carry it over to next year."