Melbourne fell short of a win but pushed the Chiefs and their case to remain in next year's Super Rugby competition with a gutsy 27-14 loss at AAMI Park.

With rumours continuing to swirl that the Rebels might be cut from Super Rugby in 2018, they delivered their best showing of the season against the unbeaten Chiefs - rated among the title favourites.

After leaking 127 points in their opening two games, the winless Rebels regrouped after the bye and put their bodies on the line to push the visitors to the wire.

They scrapped for every ball, with their flankers Jordy Reid and Colby Fainga'a getting the better of the Chiefs at the breakdown.

However, Chiefs flanker Sam Cane collected the points when it counted, scoring in the 77th minute to seal the hard-fought victory, before Shaun Stevenson added a bonus-point try before the final whistle.

The Rebels trailed 7-3 at halftime after three missed penalties by Reece Hodge but hit the front three minutes into the second half through winger Marika Koroibete.

The former Melbourne NRL flyer ran onto a cutout pass from five-eighth Jackson Garden-Bachop and dived across in the corner for his first Super Rugby try.

The home side pushed that out to 11-7 through a Garden-Bachop penalty and had their tails up.

But the Chiefs, who had to overcome two yellow cards, played a patient game and started to grind Melbourne down.

They took the lead through Test lock Brodie Retallick after a rolling maul, before the Rebels levelled at 14-14 with another penalty.

However, at the business end, Melbourne weren't able to go with the Chiefs, with Cane and then Stevenson's late effort making the victory a comfortable one.

While proud of his team's improved performance Rebels coach Tony McGahan said they had forgotten about the result.

"We've lost the game but during the week I said we were really looking for a performance to build on after the last two weeks and the players delivered on that," McGahan said.

He said they still needed to do more to have an impact on the competition.

"We're going to have to be better than that," McGahan said.

"We were slow out of the blocks and now we're on the road and we need to make sure we're getting better."

Chiefs skipper Sam Cane said the only positives his team could take from the match were the competition points and the last five minutes and felt they "won ugly".

He gave credit to Melbourne for that.

"We knew the Rebels had conceded a fair few points and then with they would have been working hard to get things right and we got exactly what we expected," Cane said.

"They really took it to us for the majority of the game and put us under lots of pressure - they were physical and direct and to be fair we struggled with that."