Valley ended a busy seven days with a heavy home defeat against a strong Sky Blues line-up in the Birmingham Senior Cup.
City sent a side to Butlin Road with plenty of first team experience in the regional knock-out trophy, and their levels of ability were too much for Valley.
Michael Rose, Max Biamou and Amadou Bakayoko - who were all part of City's EFL squad at the weekend - had great opportunities early on, before Charlie Wakefield scored the visitors' first when his shot left Matt Hill wrong-footed.
Bakayoko made it two when he closed down Hill's attempted upfield clearance to guide the ball home from an angled position and then Rose looped a header in from close range.
Dylan Parker snatched one back for Valley ahead of the interval, with a decent low finish after he had nicked possession from Tennai Watson.
Hill denied Biamou early in the new period and Jack Burroughs sent a good chance over as Coventry threatened to add to their tally, before poor Town defending presented Biamou with his side's fourth.
Zain Westbrooke rounded off the scoring from the spot in the 85th minute after Jamal Clarke had fouled Will Bapaga in the box.
Liam Francis's looping header and Caine Elliott's blocked shot represented Rugby's two main chances of the second half.
Line-up: Hill; Koriya, Evans, Clarke, Francis; Hayden, Elliott, Seal (Lockley); Marsden (Kavanagh), Parker, Luckie (Padmore). Subs not used: L.Recci. Booked: None.
Coventry Line-up: Ben Wilson, Tennai Watson, Morgan Williams, Michael Rose, Sam McCallum, Josh Eccles, Charlie Wakefield, Zain Westbrooke, Amadou Bakayoko, Max Biamou, Gervane Kastaneer. Subs: Declan Drysdale, Tom Billson, Jack Burroughs, Will Bapaga, David Bremang.