In a Big Bash League match dominated by the ball, the Renegades looked set for an easy win after racing to 0-38 after four overs in reply to the Scorchers' meagre total of 7-117.
But Arafat, who only arrived in Perth on Monday after getting a late call to replace West Indies opener Dwayne Smith, turned the match on its head when he came on to bowl in the fifth over.
The Pakistan paceman claimed 3-15 off four overs as the Renegades limped to 8-111 off their 20 overs.
The Renegades needed a six off the final ball to send the match into a bowl-off, but Andrew Fekete failed to connect with Alfonso Thomas' delivery.
Not one six was hit in the match.
The result leaves Melbourne Renegades winless after two games, while the Scorchers improved their record to 1-1.
Renegades paceman Nathan Rimmington was at his stingy best with the ball, snaring 2-14 off four overs.
But his night was nearly over after his first over when he hurt his knee after sliding into the stumps while retrieving a teammate's throw.
Rimmington limped away to assess the damage, but returned in style to claim two wickets in a magnificent display.
Scorchers openers Simon Katich (29) and Shaun Marsh (31) got off to a good start to lift the home team to 0-42 after five overs.
But the runs dried up from that point on, with the Scorchers going 14 overs without a boundary as spinner Muttiah Muralitharan (1-13 off four) and paceman Rimmington (2-14 off four) applied the clamps.
The Renegades came out firing in their run chase, but had to temper their game plan after openers Aaron Finch (15) and Alex Doolan (21) got out in quick succession.
When Scorchers allrounder Mitch Marsh (2-15) dismissed Ben Rohrer and Jos Butler in his first over, and Thomas chipped in with a scalp, the Renegades were looking shaky at 5-77 after 14 overs.
Things continued to go wrong for the visitors, with runs hard to come by on a slow WACA wicket.
Man-of-the-match Arafat revealed he had received crucial local advice from Thomas and coach Justin Langer.
"They told me where to bowl," Arafat said.
"The ball was seaming today, so the plan was to bowl up to the batsmen rather than bowl short, which paid off.
"Three days ago I came from Pakistan.
"It's a very nice feeling for the team and for me to get man of the match in the first game."
Arafat said the 15,953 crowd helped pump up the team when things weren't looking so good.