Melbourne's quest for Super Rugby Pacific redemption has fallen just short, with the Rebels going down to the Chiefs 33-30 in a Sunday afternoon thriller.

Prop Ollie Norris brushed off tacklers to score for the Chiefs in the 80th minute to deliver heartbreak for the home side at AAMI Park.

Melbourne were looking to rebound from a 43-point thrashing by the Blues and while they didn't get the win they at least did plenty to earn back respect.

Their loss meant a clean sweep of Australian teams by their Kiwi rivals through round 13 with the Chiefs moving into fourth spot on the ladder while the Rebels sit outside the finals in ninth.

"There's a lot to like about that," said Melbourne coach Kevin Foote.

"The most positive thing is our character.

"We had a theme for the week 'Man in the Mirror' -- look at yourself in the mirror -- and I think the boys did that brilliantly."

Foote revealed five-eighth Carter Gordon had managed only one training session due to the flu which hit half his team over the past two weeks.

Chiefs skipper Sam Cane said his finals-bound side "got out of jail", and coach Clayton McMillan agreed.

"We're just struggling a bit at the moment for some continuity in our game," McMillan said.

"I look at the last two or three minutes, and the speed and accuracy with which we played, the urgency, to get the try that ultimately sealed the match.

"We need to do that for longer because at the moment we're in and out of games too often."

Melbourne took the lead in the 71st minute with Reece Hodge slotting a penalty to put his team ahead 27-26 and then extended it six minutes later with another.

But the four-point buffer wasn't enough.

Chiefs five-eighth Josh Ioane, returning from five weeks out with a rib injury, was hero and villain for his team, setting up three of their tries but also gifting the Rebels two.

Melbourne led at the 47 minute mark after scoring two tries while they were a man down, with prop Pone Fa'amausili given a yellow card for some off-the-ball antics following a massive hit on Chiefs lock Naitoa Ah Kuoi.

Ioane threw a loose pass that was toed ahead by Rebels winger Andrew Kellaway for a try.

And just before halftime Rebels five-eighth Carter Gordon also intercepted an Ioane pass and dashed 80 metres to touch down.

But the Chiefs again nudged ahead 19-17 in the 57th minute when hooker Samisoni Taukei'aho drove across the line, with Ioane adding the extras.

It looked like the men from Hamilton might run away with the match after centre Emoni Narawa danced through some traffic to open up a nine point lead.

The Rebels rallied but the late try meant they still came up short.

Wallabies playmaker Matt Toomua is on track for their trip to Wellington to face the Hurricanes after missing the past three weeks following a head knock.