Jamie Donaldson (69) and Steen Tinning (68) shared fourth place at 10-under- par 270.
Lafeber became the third Dutch player to win on the European Tour and the first home player to capture the Dutch Open since Joop Ruhl in 1947.
'It feels incredible,' said Lafeber. 'I wanted to win so badly the last few months and to win this tournament means so much to me. To be playing here is great and even winning is just incredible. The support I had was unbelievable for four days.'
Hansen, who played with Lafeber in Sunday's final pairing, held a one-shot lead heading into Sunday's final round but extended his lead with a 10-foot birdie putt at the second and a tap-in birdie at No. 3.
Lafeber knocked a 4-iron 20 feet left of the hole at the sixth and made the birdie putt to cut the deficit to two shots. Hansen dropped a shot at the par-4 eighth to hold a one-shot lead but the par-4 ninth proved to be a critical hole.
Hansen drove into the left rough and had to hook his second shot around a tree to try and hit the green. His ball never came around and his approach landed 30 yards right of the green behind a tree. Hansen's third never reached the green and he pitched his par chip ran home nine feet past the hole.
Lafeber knocked his second less than three feet from the hole and Hansen missed his bogey-saving putt. Lafeber sank his short birdie putt and the three-shot swing gave Lafeber a one-shot lead over Gronberg and a two-shot edge over Hansen.
Gronberg, playing several groups ahead of the final pairing, squandered opportunities at the par-5 12th when he three-putted for par and at 16 when he landed in a bunker and failed to get up and down for par.
The battle was down to Lafeber and Hansen with Gronberg in the clubhouse. Hansen left a 30-foot eagle try at the 12th on the lip but tapped in for par cutting the margin to one. Lafeber made birdie on the hole to go up by two and the lead became three when Hansen missed a short par save at the 13th.
Hansen birdied the 14th to get within two and rolled in a six-footer for birdie at the 16th to creep within one of the lead. Both players had good looks at birdie at the 17th but neither converted so it was on to the closing hole, a par-5, at Hilversumsche Golf Club.
Hansen hit a long drive down the fairway at 18 and Lafeber drove into the first cut of the left rough. Lafeber came up just short of the green with his second while Hansen sprayed his second right of the green.
Lafeber chipped up to four feet and Hansen took a run at the bottom of the cup. Hansen played his shot far too left of the hole and had nine feet for birdie. He missed that putt and opened the door for a two-putt victory for Lafeber.
Lafeber took that many putts but still earned his first title on tour.
'I was so glad not to have to make that putt on the last,' admitted Lafeber. 'Tension was building up. Soren played really well. It was a rough day but I played really solid.'
Hansen finished with a 1-under-par 69 while Gronberg made the biggest move of the day with a 5-under 65 to tie at 12-under-par 268.
'I was hoping to play 5- or 6-under and see what could come with it,' said Gronberg. 'Top-5- I would taken that before the day started. I wasn't really happy with my swing today and I had some really good breaks.'
Alastair Forsyth (67), Gary Evans (68) and Gary Murphy (70) shared sixth place at minus-9, followed by Miguel Angel Jimenez, Fredrik Andersson, Stephen Dodd, Gary Emerson, Kenneth Ferrie and Adam Mednick, who tied for ninth at 8-under-par 272.