Anthony Wall (65), Mark Mouland (67) and Paul McGinley (68) shared fifth place at 17-under-par.
Rose was tied for the lead at 17-under with Foster and Ernie Els as he stood on the par-3 15th tee. He roped his 5-iron approach at the 225-yard hole to two feet to set up birdie and reach 18-under for the tournament.
A hole behind at No. 14, Els found trouble off the tee. He took a double-bogey at the 14th and then a bogey at No. 15, falling out of the tournament and finishing alone in ninth at 15-under-par, one shot behind Sandeep Grewal.
Foster and Maritz played the 14th very differently in the last group. Foster bogeyed the hole to fall to 16-under while Maritz holed his approach at the hole to get to 15-under for the tournament.
Rose held a one-shot lead at 18-under-par when he missed the green left at the par-5 16th. He blasted his third to tap-in range to card his second birdie in as many holes and move to 19-under, which gave him a one-shot edge over Goosen, who reached the clubhouse at 18-under.
Rose, who was born in South Africa but moved to England at the age of five, parred No. 17 but was feeling the heat as Maritz eagled the 16th and birdied the 17th to get within one of Rose's lead. Foster birdied Nos. 15 and 16 to also get to 18-under as the stage was set for Houghton Golf Club's closing hole to determine the outcome.
The 21-year-old chipped his third at the final hole inside a foot to card his third birdie over the final four holes. He reached 20-under-par, the same score he posted last year when he fell one shot shy of Adam Scott, and watched as Foster and Maritz both missed eagle chips.
'There was a couple of key moments where I was brave and pulled the trigger, especially at the 16th,' said Rose. 'I just kept saying to myself: Justin, youre a winner. You are going to win this week. Its your turn.'
The win was Rose's first on the European Tour. He came close last season, not only losing by a stroke to Scott at this event, but also taking a second at the South African Open.
Rose burst on to the scene at the 1998 British Open. He holed out a chip that gave him a fourth-place finish as an amateur and turned professional the next day. Rose missed 22 consecutive cuts on the European Tour after that but he never lost his resolve to win.
'I've always believed deep down I have the talent,' he said. 'But my family's support really helped me through all those missed cuts. I never lost belief. I knew it would come right and it has.
'I wanted my first win to be the one which stops people just remembering me for Birkdale. But, in a way, I feel all those missed cuts I had prepared me for this moment.'
Goosen fired a final-round 65 but he knew before the round started that score might not be enough.
'I thought I needed a 63 and so it proved,' said the 2001 Order of Merit champion.
Foster, the European Challenge Tour champion last year, carded a 69 but the bogey at No. 14 stopped him from earning his first title on the European circuit.
'I put myself in contention and it was another good week,' said Foster, who took fourth at the Omega Hong Kong Open in November.
Maritz, the third-round leader, struggled to a one-under 71 on Sunday.
Full-Field Scores from the Dunhill Championship