Struver initially had a birdie on the last hole to force a play-off with Swede Patrik Sjoland, then produced another birdie on the 18th - the first extra hole of sudden-death - to win the tournament.
Both Struver and Sjoland had finished on 21-under-par 263, two shots ahead of playing-partner Darren Clarke of Northern Ireland, after carding 66 and 70 respectively.
Struver had started the last round four shots behind the Swede but wiped out the deficit by following up his two eagle-twos on the third round with another on the 290-yard seventh.
A drive onto the green, guarded by the Matterhorn, put the squeeze on Sjoland but the Swede, despite missing three short birdie putts, then moved three shots away from Struver with three successive birdies from the ninth.
However, with the finishing-line in sight, Sjoland faltered with two more bogeys and was caught again. Even then, he edged back one in front with a birdie at the 17th.
Yet Struver was not to be denied, seizing a birdie at the last, and when he and Sjoland faced 10-foot putts at the first extra hole, it was the German's which went to ground.
"I've never won in a sudden-death before so it's a good way to add my third title," said Struver, the son of a teaching pro. "I came from seven shots behind Ernie Els to win my first, the SAPGA Championship, so that was pretty memorable, but this was real excitement.
"I thought I'd need to shoot 63 or 64 to beat Patrik and wouldn't have thought 66 was good enough, but the key was definitely the 18th. I played it five times altogether and birdied it four times."
Three missed putts of around the five-foot mark before getting back on a roll, and then failure to master the late par-fives, cost Sjoland his second win of the year.
"Sadly I couldn't hole short putts on six, seven and eight, which just shaved the hole, and the back nine par-fives were the key to losing in the end," said the Swede.
Clarke birdied four of the last five holes, but a double-bogey on the short third denied him his chance of a play-off, and the pounds 50,000 he earned was not enough for him to top the European rankings.
That was because England's Lee Westwood closed with a 68 to earn a share of 12th place and keep Clarke pounds 5,498 short of overtaking him.
Colin Montgomerie would have been overtaken for third place in the rankings if Sjoland had prevailed, but the Scot kept his spot, despite double-bogeying the last for the second day running, also to share 12th.