The South African entered the final day at Golfclub München Eichenried four shots behind his rival but had reeled him in by the turn before back-to-back three-putts on the 12th and 13th left him two behind with five to play.
The 17th then proved critical as Lawrence hit a stunning tee-shot to set up a birdie and Luiten three-putted the par-three to drop out of the lead for the first time all day.
Lawrence parred the last for a 69 to finish at 13 under and with Luiten unable to make a birdie on the par-five, the 26-year-old was left celebrating a fourth DP World Tour title.
Luiten's closing 74 left him a shot ahead of Kiwi Daniel Hillier, Japan's Rikuya Hoshino, local favourite Maximilian Kieffer and Pole Adrian Meronk.
Lawrence was the first winner of the DP World Tour era last season at the Joburg Open and he added another title at the Omega European Masters en route to being crowned the Sir Henry Cotton Rookie of the Year.
Another win in his homeland at the Investec South African Open Championship came at the start of this season but that was his last worldwide top ten and Lawrence cut an emotional figure as he reflected on a fourth win in 19 months.
"It means a lot," he said, fighting back tears after becoming just the second South African to win this trophy after the great Ernie Els.
"There's been a lot of hard work. I went to America for six weeks and made one cut - this game is not easy. It was a real boost today and I really gave it my all. I feel sorry for Joost, I know how tough this game is.
"I don't know why I'm so emotional but obviously it just shows that it means the world and to get my fourth victory in Germany is unbelievable.
"I seem to win a lot of events that Ernie has won. It's special, he's obviously the ultimate hero for me. I grew up in that era where he was on top of the world and it's very special to to get my name along alongside him."
Lawrence holed a 46-footer at some pace on the second and followed it with a left-to-righter from 23 feet on the next to get within two of the leader after a quick start.
A Luiten three-putt on the third saw the lead down to one but Lawrence found the hazard on the fifth and had to take a drop, surrendering his first shot of the day.
The advantage was up to three as Luiten holed from 17 feet on the fifth but Lawrence got up and down on the par-five sixth and then hit a wonderful approach to four feet at the next to trim the advantage back to one.
Lawrence missed the green at the eighth to give up a bogey but Luiten three-putted again from the fringe at the seventh and a Lawrence birdie after laying up at the par-five ninth had him tied at the top.
The roller coaster continued for Lawrence when he found sand and dropped a shot at the tenth and, after it had been a two-horse race over the front nine, there were now five players within three shots of Luiten.
Lawrence was back in a share of the lead after laying up at the par-five 11th but back-to back three-putts dropped him two behind and all of a sudden, Kieffer was the nearest challenger.
He had birdied the first after a smart approach but gave the shot back on the the third before making it birdies on all four days at both the sixth and ninth to turn in 34.
He continued his remarkable record on the par-fives with an eagle from 28 feet at the 11th and an approach to ten feet had him within one before he found water at the 16th and dropped a shot.
That gave Luiten his two-shot cushion back but it would not last for long as Lawrence holed a remarkable 36-foot left-to-righter that went over a mound and through the fringe on the 15th before he put his tee-shot to five feet at the 17th for an eighth birdie of the day.
There were then gasps around the 17th green as Luiten missed from three feet and a third three-putt of the day meant that, for the first time in the round, the Dutchman was off the top of the leaderboard and needed a birdie up the last for a play-off after Lawrence finished his round with just a fifth par of the day.
Luiten hit a tree off the 18th tee which forced him to lay up and while he had a chance to birdie from the fringe, he missed from 25 feet and Lawrence was the victor.
Kieffer carded a 68, the same score as Meronk, with Hoshino signing for a 69 and Hillier recording a 71 to finish a shot ahead of Dutchman Daan Huizing, Dane Rasmus Neergaard-Petersen and Frenchman Matthieu Pavon.