The Ducati man was at the front of the field when he fell with 16 laps to go before championship leader Rea, who is on 235 points at the top of the standings, also went down with three laps remaining.
Sykes clinches victory at Donington Park
Davies picked his Ducati up to rejoin the race and eventually finished eighth, but the result will be a big blow to the Welshman's world title aspirations.
Jonathan Rea fastest in race two at Donington
Rea was denied a podium finish when he crashed out of the race, although the Northern Irishman was soon back on his feet and taken back to the pits on a scooter.
Sykes finished in style to continue his Donington domination and cut Rea's championship lead to 50 points, with wildcard Leon Haslam (Kawasaki Puccetti Racing) and Alex Lowes (Pata Yamaha Official WorldSBK Team) making it an all-British podium..
Rea crashes out at Donington after rear wheel failure
The second race of the championship's UK round will be held on Sunday afternoon.
Haslam, Lowes involved in early crash as Race 2 red-flagged
Tom Sykes hospitalised after heavy crash in Catalunya, suffers concussion but nothing else