Ellis pulled out from Wednesday afternoon's clash at Ninja Stadium with illness, but his bowling teammates stood up against the table-topping Sixers.
The Hurricanes posted 6-161 and bowled out Sydney for 111 in 19.3 overs to jump to fourth on the ladder with a third win in a row.
Import Chris Jordan picked up 3-22, including the big scalps of James Vince (11) early and noted finisher Jordan Silk (20) in the middle overs.
He was assisted by Afghanistan's Waqar Salamkheil, who took 2-22 with his left-arm wrist spin and bowled Kurtis Patterson with one that turned the other way.
Hobart allrounder Nikhil Chaudhary was impressive, top scoring with 42 from 31 deliveries and picking up 1-15 with the ball.
The Sixers, who stay in first place on the ladder, had won four from four prior to the match, while the Hurricanes are on the rise after being flogged by the Renegades in their opening game.
"We got to know (about Ellis) a couple of hours before the game," Chaudhary said.
"It was a huge loss for us but at the same time he was texting us (saying) 'doesn't matter if I'm playing or not'.
"He's that kind of person … he wasn't playing but he was behind us from home.
"We're looking forward to getting him back in the team."
Veteran Sydney Sixers bowler Jackson Bird took 4-16 against the Hobart Hurricanes in the BBL. (Dan Himbrechts/AAP PHOTOS)
Earlier, evergreen Sixers quick Jackson Bird took career-best Twenty20 figures of 4-16 on familiar turf in Hobart after his side won the toss and elected to bowl.
The 38-year-old, who played for Tasmania for more than a decade, removed big hitters Matthew Wade, Shai Hope, Ben McDermott and Tim David.
Returning from a calf injury, Wade was scratchy in a 16-ball 15 and became Bird's first victim off a nifty caught and bowled.
Bird had West Indian import Hope caught behind two balls later as the Hurricanes lost 3-10.
McDermott (34 from 25) came to life in the power surge, hitting 20 off one Hayden Kerr over but he was undone by Bird, who also returned late to get rid of David via a top edge.
"The old fellow keeps churning them out. He's actually bowling through the phases ... he's not just an opening bowler," Sydney coach Greg Shipperd said.
Sydney's chase had a bright spark early when English opener Vince launched a Billy Stanlake delivery over the hill but they wobbled to 3-28 inside the first five overs.
"That was probably one of our worst performances in a long time," Shipperd said.
"(But) that can happen in a T20 game. It was a collective out for our batting group which is a very rare occurrence."
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