Vaz Te had a goal ruled out by referee Andy D’Urso after 13 seconds for a push on Pascal Chimbonda, a decision Allardyce believed was incorrect, before Carlton Cole crashed a volley against the bar.
The breakthrough arrived in the ninth minute, Nolan stabbing home after Carl Ikeme had made a spectacular save from James Tomkins’ header.
However, the lively Vaz Te then had to be withdrawn, and with West Ham’s attack blunted Doncaster soon grabbed a foothold.
Rob Green tipped Simon Gillett’s long range drive wide and saved at his near post from Habib Beye early in the second half.
The visitors deservedly levelled in the 73rd minute, Coppinger pouncing on a loose ball in the six-yard box after Gillett had turned El-Hadji Diouf’s delivery back across goal.
Green then made a stunning save to deny Diouf seven minutes from time, before Collison blazed wide of a gaping goal in added time.
Rovers manager Dean Saunders, whose side remain 23rd, said: “We should have won. I thought we were going to get battered in the first ten minutes, but we changed the shape and looked better straight away.”