Chris Stirling’s side eked out victory - a fifth in six games in the competition - to set up a last-eight meeting against either Cornish Pirates or Bedford Blues in February.
More importantly, this latest win further built confidence ahead of their return to league action.
Carnegie have just one win so far in the Championship where they sit bottom but, with 10 signings in recent weeks now making their mark, they will look forward to the derby at Doncaster Knights on Saturday December 29 with renewed relish.
One of those recruits – New Zealand winger Elijah Niko – scored on his home debut, a second try in as many games to get them up and running.
He claimed Harry Davey’s high pass, who came in as one of five changes, and showed his class with the finish. Jade Te Rure converted for a 10-5 interval lead having earlier slotted a penalty in response to a try from former Doncaster back-row Jack Ram.
In awful conditions, young winger Davey picked up a loose ball to race in for Carnegie’s second try to extend the lead.
Coventry - who needed a win to claim top spot themselves - had their chances but the hosts defended well.
The visitors also wasted a glorious opportunity at the death, taking a quick tap penalty but then knocking on to relieve all the pressure on Stirling’s side.
“I’m delighted with the win, but not the performance,” said Stirling.
“We were way off our best, the first 40 minutes we put ourselves under a lot of pressure with silly errors and poor decisions.
“When we managed to get our hands on the ball we gave it straight back to Coventry.
“We were lucky to be ahead at half-time and made it very difficult for ourselves.
“But that’s the pleasing thing, we had the guts to fight our way out of that difficult position.”
Focus now turns to the league where Carnegie remain in a dire situation.
Stirling added: “Pleased with a home tie, we’ll flick the switch very quickly to Doncaster now and getting back into the Championship.
“Our mission it to get off the bottom of the table, but that’s five wins out of six games now so we’re starting to turn a bit of a corner.
“We’re lucky in our group that our rivals have been playing full-strength teams and we’ve beaten them all, which gives us a little bit of confidence that going back into the Championship we can compete.”
Carnegie’s Under 18s, meanwhile, started their season with a 31-12 win over Worcester Warriors in their Premiership Under 18s opener.