The Danish striker put Preston ahead inside the first minute before setting up top scorer Will Keane and then forcing Bobby Thomas to put through his own net.
The remarkable victory took Preston on to the cusp of the play-off places, two points behind Hull, as North End leapfrogged Coventry in the process.
Preston captain Alan Browne played his corner to Ben Whiteman inside the first 60 seconds, and the cross was met by Riis.
The target man outmuscled Thomas and thundered home a header to claim his fourth in four outings after failing to find the net this season until 13 days ago.
When the 25-year-old then saw a shot blocked by Thomas he took full advantage of the dawdling Jay Dasilva and stole in to tee up Keane, who reacted fastest to sweep home his 12th of the season in the 20th minute.
The Sky Blues had failed to beat Preston in their last 20 league meetings dating back to 2007, and things went from bad to worse when winger Tatsuhiro Sakamoto was taken off on a stretcher after a heavy fall following a challenge by Andrew Hughes on the half-hour mark.
The Japan international had been one of two Coventry changes as he and Milan van Ewijk replaced Fabio Tavares and Victor Torp in the starting XI, while Ali McCann came in for Robbie Brady in a rare Preston change.
Coventry had only lost once at home since a 4-0 thrashing by Stoke last April and things looked to be heading that way once again when Thomas poked Riis’ cross past a helpless Ben Wilson.