The duo finished regulation tied at 8-under-par 272 as many of the leaders during the back nine Sunday faltered down the stretch.
Scott Petersen and Mike Sullivan shared third place at 7-under-par 273. Michael Muehr, Emlyn Aubrey and Jason Dufner tied for fifth at 6-under-par 274.
At the first playoff hole, the 18th at Hardscrabble, Haskins drove into the deep rough off the tee and could only advance his ball 100 yards short of the green in the left rough.
Johnson found the fairway on the first extra hole and played his second 15 feet from the hole on the fringe. Haskins knocked his third shot 20 feet over the flag and missed his par-saving putt.
Haskins would not have another chance to putt. Johnson calmly two-putted for his first win on the Nationwide Tour.
'This is unbelievable,' said Johnson, who shared third last week at the First Tee Arkansas Classic after holding a piece of the 54-hole lead. 'I was kind of down after last week but I've been playing well. I took a lot of what happened into this week, especially with composure and patience.'
'The playoff happened so quick,' said Haskins, who is the Nationwide Tour's all-time leader in starts. 'I didn't make a good swing off the tee and my next mistake was not getting out of the rough.'
Johnson fired a final-round, 4-under 66 as Haskins shot an even-par 70 on Sunday.
Johnson teed off an hour before third-round leader Franklin Langham. He quickly flew up the leaderboard with a birdie-eagle-birdie stretch starting at the second hole.
'I got off to a great start and I just kind of went with it,' said Johnson. 'I definitely thought I had a chance. I felt great today.'
Johnson was still chasing several players when he reached the par-4 14th. He punched a 7-iron from 180 yards to a foot to set up birdie and get to 8-under par.
He parred his final four holes and watched as the other players that were ahead of him fell backward.
Langham drove into the trees at 14 and didn't reach the fairway until his fourth shot. He nearly found water left, then hit a bad chip and two putts later Langham was done. He shot a final-round 76 and tied for 12th at 4-under-par 276.
Dufner bogeyed three of his final six holes, Aubrey made double bogey at 14 and Sullivan made seven pars in a row to close his round but needed another birdie somewhere.
Omar Uresti (67), Hunter Haas (69), Tom Carter (71) and Boo Weekley (71) shared eighth at 5-under-par 275.