Heavy-hitting Josh Brown top-scored with 84 off 48 deliveries for the Renegades, putting them in the box seat before a late collapse at the MCG on Sunday night.
The Renegades lost 5-34 in less than five overs and required 13 off the final six balls when Sutherland faced up to Stoinis.
Sutherland (19 not out off seven) stepped up when needed, twice sending Stoinis over the rope as the Renegades reached 6-177 and chased down their target with just one ball to spare.
"It was a bit of a dream come true as a Melbourne boy," Sutherland said.
"I've been at the Renegades for a long time and this was a lot of fun.
"I was just trying to watch the ball and react to where it was supposed to go, and a couple came off, which is always nice."
The epic finish played out in front of 68,124 fans - the third-highest attendance in the BBL's 15-year existence.
Melbourne derbies have provided the top four attendances in the competition's history, including a record 80,883 in 2016.
"Huge night," Sutherland said.
"I'm happy for Victorian cricket that this many people are showing up to the derby and it's always nice to beat these guys.
"It's a real rivalry and I'm glad we could get the first one of two over them (this season)."
The Renegades started their run-chase well, scoring at better than 10 an over in the opening powerplay, and looked in control when Brown and Mohammad Rizwan (41 off 38) added 29 runs in the power surge as part of a triple-figure partnership.
Their side was cruising at 1-127 after 14 overs, but the Stars had a sniff when Mitchell Swepson (1-20) bowled Brown and breathed life back into the contest.
Haris Rauf (2-44) and Peter Siddle (2-39) also struck blows that looked like helping the Stars over the line before Sutherland's heroics.
"We probably should've chased it with two overs left to go, but it's good to have takeaways and still win the game," Sutherland said.
"Our batting hasn't quite clicked and that showed again tonight, but we're not far off.
"We spoke about a 75-plus score, which Josh Brown was able to do, and he batted beautifully."
It was the Renegades' (2-3) second victory of the season, ending a three-match losing streak, while the Stars (4-2) have lost two in a row after winning their first four.
Sent in to bat, the Stars saw regular wickets fall in their 9-172, with veteran matchwinner Glenn Maxwell (one off four) out cheaply.
Late hitting from Tom Curran (38 off 18) and Campbell Kellaway (33 off 27) helped them to a competitive total.
Renegades seamer Gurinder Sandhu (4-41) combined with spinners Callum Stow (2-24) and Hassan Khan (1-26) to inflict most of the damage to the Stars' top order.
Swepson praised the Stars' determination, lauding Stoinis for rallying his troops as they mounted a fightback late in the Renegades' innings.
"It was great to see the fight, even when they were one-for and didn't need many, we put up a really good fight and kept coming at them," Swepson said.
"We kept making it really hard for them to score runs and that's why it got down to the last couple of balls."
TOP FIVE BBL ATTENDANCES
80,883 - Stars v Renegades (MCG) January 2016
71,162 - Stars v Renegades (MCG) January 2017
68,124 - Stars v Renegades (MCG) January 2026
54,478 - Stars v Renegades (MCG) January 2020
53,886 - Scorchers v Heat (Optus Stadium) February 2023
