But the visitors rallied back after the break and snatched their equaliser when Kieran Djilali slotted home from close range, giving their fans hope amid intense speculation Warnock is set to take the reins at QPR.
Doncaster, who themselves headed into the game following back-to-back defeats, were without captain Brian Stock after the midfielder's old back problem returned, while Martin Woods was also missing from the middle of the park due to a groin injury and defender Shelton Martis was out with a hamstring problem.
Rovers had on-loan Arsenal midfielder Jay Emmanuel-Thomas on the bench following his move this morning, while Sam Hird was added to a five-man defence.
Palace boss Neil Warnock made two changes from Wednesday's 3-1 defeat to Aston Villa in the FA Cup, with Clint Hill and Djilali taking the places of Johannes Ertl and Neil Danns.
He was forced into a further change to his side after just six minutes when defender Claude Davis was forced off due to injury, paving the way for an early introduction for youngster Lee Hills.
The hosts made an encouraging start, with Billy Sharp heading wide from close range before James Hayter slashed wide after latching onto a Coppinger corner.
Rovers saw another decent early chance go begging when James Hayter's strike was collected comfortable by Argentinian stopper Julian Speroni.
John Oster then fired wide twice before the hosts finally made their dominance pay in the 37th minute.
Some good work around the edge of Palace's box created an opening for Coppinger to drive home from 18 yards.
James Chambers then struck wide from a similar range before Mark Wilson and Coppinger were denied by Speroni.
Warnock took substitute Hills off at the break with Ertl sent on, and the Palace boss saw his side look livelier after the restart with Darren Ambrose and Nick Carle sending attempts off the target.
Palace came closer on the hour mark with Shaun Derry's close-range strike blocked by Hayter.
Their efforts after the break were rewarded in the 67th minute when Darren Ambrose ended a mazy run with a pinpoint cross allowing Djilali to slot home from six yards.
Ambrose could have then added to his assist with a goal of his own but failed to beat Speroni with his close-range strike.
Rovers looked to reassert their dominance with Sharp's powerful strike forcing Speroni into action before Hird headed wide.
Substitute Emmanuel-Thomas then also tested Speroni with his long-range strike before Ertl volleyed over at the other end.