Last season's Championship winners had started brightly on Saturday, summer signing DJ Campbell seeing an effort ruled out for offside, before Dyer, signed on a free transfer from West Ham, fell awkwardly and had to be carried off with a reported broken metatarsal.
Bolton took the lead on the stroke of half-time with a fine curling effort from centre-back Gary Cahill.
An own goal from Danny Gabbidon, making his debut, and Ivan Klasnic's deflected strike effectively had settled matters ahead of a fourth for Fabrice Muamba following a swift counter-attack with 11 minutes left.
QPR defender Clint Hill was shown a red card in stoppage time.
Some of the 15,000 home support headed for an early exit, venting their frustrations at shareholder Flavio Briatore, who could soon sell up to Lotus Formula One boss Tony Fernandes, watching from the director's box.
Things could have been so different had Campbell, who impressed for Blackpool last season, not seen his early close-range effort disallowed.
Then, on five minutes, Dyer, who has completed 90 minutes only once in his last 29 Premier League matches, stretched for a 50/50 challenge and landed awkwardly, leading to extensive treatment before the former England midfielder had to be carried off on a stretcher, his foot already in a protective boot.
Bolton, who faded badly after their FA Cup semi-final defeat last season, soon settled, with new arrivals Nigel Reo-Coker and Chris Eagles both playing well in midfield.
On the stroke of half-time, they were ahead when Eagles fed Cahill, who had stayed up from a corner.
The centre-back, a target for Arsenal, took one touch before curling a sublime effort into the top left corner.
After 56 minutes, QPR captain Adel Taarabt, who has been linked with a big-money move away during the summer, finally found some space on the edge of the Bolton area, but his shot flew wide.
Bolton, though, were 2-0 up after 68 minutes.
Davies won a free-kick when bundled over by Alejandro Faurlin just outside the area on the left.
Eagles low delivery was deflected off the wall and across the six-yard box towards the far post, where Gabbidon put the ball into his own net.
Before QPR could mount a recovery, Ivan Klasnic made it 3-0 when he drilled home via a deflected effort off Bradley Orr after a knockdown from Davies.
Warnock made a double change on 72 minutes, replacing Tommy Smith and the disappointing Taarabt with Heidar Helguson and Akos Buzsaky.
Cahill was booked for tripping Shaun Derry on the edge of the Bolton penalty area, but Buzsaky hit the free-kick into the wall, which just about summed up Rangers' afternoon.
Fabrice Muamba swept in number four after a flowing counter-attack and QPR's miserable day was compounded when Hill was shown a straight red card for pushing his head into Petrov's chest as the pair tussled on the near touchline during stoppage time.