Bolton, too, remain in line for a UEFA Cup spot despite conceding three times in the last six minutes.
Nicky Shorey's own goal after help from Nicolas Anelka put Sam Allardyce's team in front after 64 minutes.
And it looked certain to clinch three vital points for the Lancastrians until Doyle's late double.
Coppell revealed the Irishman hadn't trained all week to protect his groin problem, but he drilled home an 84th minute penalty when brought down needlessly by Abdoulaye Meite.
Four minutes later, Doyle knocked in his second when Meite lunged in on Steve Sidwell and the ball broke to the Royals top-scorer.
And in the last seconds an unmarked Stephen Hunt headed in Reading's third from a left-wing cross.
It was an amazing and exciting finish to a game that, up to that stage, had largely been second rate.
Bolton certainly didn't deserve to lose and a draw would probably have been a fair result.
Indeed, Wanderers could be without three key players for their final three games as Nicky Hunt (calf), El Hadji Diouf (hamstring) and Kevin Nolan (ankle) all failed to finish the first half.
Allardyce has consistently bemoaned his team's inability to convert scoring opportunities and Wanderers wasted two early on when a goal may have put a different complexion on a free-kick strewn encounter.
Diouf made a weak connection to a second minute chance that Marcus Hahnemann easily saved and it was a similar tale when Kevin Davies closed in on the target.
The stream of injuries and petty offences wrecked the game as any kind of spectacle.
But Bolton were the more productive and Anelka curled a right foot effort wide, while Andranik Teimourian drove a 20-yard volley straight into Hahnemann's hands.
Doyle flicked a header that Jussi Jaaskelainen comfortably gathered as Reading offered a token threat.
With Hunt and Diouf already out of action, Bolton lost skipper Nolan on the stroke of half-time after clashing with Michael Duberry.
They did well to recover from the setbacks and were good value for their lead at the end of a five-man move.
But they reckoned without Reading's never-say-die attitude and Doyle's happy knack in front of goal.