Alker fired a bogey-free round of 8-under 64 to take the clubhouse lead with a tournament-record score of 24-under 264. Heinen, who matched the 18-hole course record in Round 3, was two shots off the pace but ran home back-to-back birdies from the 16th to force a playoff.
The duo went back to the 18th for the first extra hole and neither golfer faired well off the tee as both drives found the water.
Alker had 220 yards to the green for his third shot and came up short of the putting surface. Heinen also missed the mark and sent his ball over the green.
Heinen, who lost the 1995 Freeport-McMoRan Classic to Davis Love III in a playoff, chipped his fourth shot to within three feet of the cup while Alker's fourth left him with a seven-foot bogey try.
Alker missed his putt and tapped in for double-bogey to open the door for Heinen. However, Heinen failed to convert the short putt en route to a double-bogey of his own and the pair returned to the tee to give it a second try.
This time both players avoided the water. Alker's drive went straight down the fairway while Heinen found the left rough off the tee.
Alker's approach landed on the green while Heinen sent his second shot long and was left with a 40-foot chip.
Heinen chipped to within six feet of the hole as Alker two-putted for par. Heinen had a chance to extend the playoff but his six-foot par save missed the cup.
'I've been playing well all week and thought a 63 or 64 was out there for me,' said Alker, who pocketed $81,000 for his first win. 'I didn't have it from tee to green, but my putting was pretty solid.'
Alker, who is playing his rookie season on the Buy.Com Tour, became the first player to win the Louisiana Open in a playoff.
'I let a lot of people back in it today,' said Heinen. 'I was playing it ho-hum all day. I hit the shots I needed to hit, I just didn't make any putts.'
Marco Dawson shot a seven-under 65 to finish alone in third at 22-under-par 266.
Wes Short and Keoke Cotner were tied one shot further back at 21-under 267.
Rob McKelvey, who won this event in 2000, posted a 6-under 66 to finish alongside Jason Gore at minus-20.
Full field scores from the Louisiana Open