The Clarets saw their winless run in the Championship extended to four matches on a night of frustration at Turf Moor.
Jack Cork's first goal of the season spared a second successive home defeat for Brian Laws' men.
But the midfielder's 63rd-minute equaliser was the minimum Burnley were looking for as they tried to close in on the top six in the first of back-to-back home games.
A missed penalty from Chris Eagles did little to help the Clarets' cause once they had fallen behind to a 13th minute James Hayter goal.
And with Doncaster's 40-year-old goalkeeper Neil Sullivan and his defence refusing to yield, bar for Cork's close-range header, Burnley didn't do enough to build on a promising opening and breathe new momentum into their promotion push.
The Clarets should have made a flying start as they swarmed all over the visitors.
But, indicative of things to come, twice within the opening minutes they saw things go wrong in front of goal.
Chris Eagles feels the pain of his missed penalty
After just 16 seconds Wade Elliott was released by a perfect Jay Rodriguez through-ball, but after electing to shoot early the Clarets' midfielder saw his low shot saved by Neil Sullivan, with Shelton Martis just reaching the loose ball first to clear.
Then with three minutes gone Burnley were denied an obvious penalty when the referee and his assistant somehow failed to see ex-Clarets' defender Wayne Thomas handle following a Danny Fox corner.
Hand ball? Apparently not!
After finishing on the wrong side of a contentious hand-ball decision when Norwich City pinched a late equaliser three days previously, the Clarets could be excused for rueing their luck.
And Doncaster's opening goal after 13 minutes did little to alter their view. Rovers had barely mustered an attack, but when John Oster's cross was deflected onto his own post by Jack Cork, Hayter was left with a simple tap-in.
The goal visibly unsettled the Clarets, but after re-grouping they wound up for a further sustained assault on the Doncaster goal.
Martin Paterson gets a sight of goal
Sullivan interrupted a driving run from Eagles with a timely block and then after Martin Paterson had failed to get a decent touch to a Rodriguez knock-down, Sullivan came to his side's rescue again.
This time referee David Foster pointed to the spot when Dean Shiels blocked with his hands as Eagles chipped the ball forward.
But after twice previously deputising successfully for penalty king Graham Alexander, Eagles saw his perfect spot-kick record ended as the veteran Rovers' keeper guessed right to save.
Eagles tried to make amends with a superb pass to the over-lapping Tyrone Mears, who looked certain to have created the equaliser and given Burnley the perfect tonic to take into the break when he picked out Rodriguez.
The youngster side-footed goalwards from eight yards but rather than find the back of the net the ball somehow clipped the heels of Martis and bounced to safety.
Doncaster were riding their luck but could easily have scored themselves and doubled their lead in the last minute of the first half.
Jay Rodriguez heads over as the Clarets dominate the first half
After threatening several times on the break their best chance again fell to Hayter, but from David Healy's square pass he inexplicably failed to make contact with just Lee Grant to beat.
There was an enforced change at the at the interval as the boss sent for Chris Iwelumo for the injured Martin Paterson, after the leading scorer had started on the bench.
And the big striker was immediately in the action, laying off an Elliott cross for Eagles to let fly with a shot that stung the palms of Sullivan.
Iwelumo became the focal point of the Clarets' attack as they strove to get back into the game - and it was Burnley's greater aerial threat that finally forced the breakthrough 20 minutes into the second half.
Clarke Carlisle had already headed just wide from a corner when he connected with another delivery from Eagles.
James O'Connor blocked on the line, but with Cork, Iwelumo and Duff following in, Cork just got their first to head over the line as he fell into the net.
The relief around Turf Moor was palpable - but if anything the goal breathed fresh life into the visitors for a spell and Grant was forced to make a flying save from Oster and then a block from Thomas from the resulting corner as the pair looked to punish their former club.
Jack Cork finally finds the break-through to make it 1-1
The Clarets were forced into another change as Danny Fox was stretchered off after landing awkwardly, with Alexander coming into midfield and Elliott filling in at left-back.
Alexander almost immediately teed up Carlisle for a headed chance and the defender also got a second bite of the cherry when his miscued effort was returned by Dean Marney.
But neither was taken and rather than wind up for a big finish the Clarets found themselves growing increasingly frustrated.
Their early fluency deserted them and with Doncaster comfortably holding out for five minutes of added time, and threatening late through a Thomas header, two more points quietly slipped away as the Clarets were held to an eighth draw of the campaign.
Burnley: Grant, Mears, Fox (Alexander 74), Duff, Carlisle, Cork, Marney, Elliott, Paterson (Iwelumo ht), Rodriguez, Eagles (Wallace 89). Subs: Alexander, Edgar, Cort, Thompson, Jensen.
Doncaster: Sullivan, Thomas, Stock (Hird 90), O'Connor, Shiels (Wilson 66), Coppinger, Martis, Hayter, Dumbaya, Oster, Healy (Brooker 89). Subs: Wilson, Webster, Fairhurst, G Woods.
Referee: David Foster.
Booked: Doncaster: Stock 29
Danny Fox's injury summed up a frustrating night