Rovers rallied to earn a point in a game of two halves at Ewood Park.
The home side struggled in the first half with Villa in the ascendancy, eventually taking the lead on the 24th minute when Charles N'Zogbia fired home after good work from Carlos Cuellar.
Captain Paul Robinson was in superb form, denying N'Zogbia a second just before the break and then Stephen Ireland after the restart to keep Rovers in the game.
The half-time introduction of David Dunn and Marcus Olsson swung the momentum Rovers' way, looking a different team they pressed and pressed, Given making important saves to thwart Junior Hoilett and Morten Gamst Pedersen. Yakubu and Nzonzi going close.
The deserved equaliser finally came with five minutes to go, Steven Nzonzi spreading the ball wide to Bradley Orr and his cross was met at the back post by David Dunn and he directed his header home.
A win would have seen Rovers out of the bottom three, but in the end they'll be grateful for the point after such a poor first half.
Steve Kean made one change from the side that lost to Manchester City last time.
Steven Nzonzi returned to the starting eleven after his bout of tonsillitis, Marcus Olsson the man to make way as he dropped to the bench.
David Dunn was named amongst the substitutes after recovering from a thigh injury.
Early efforts from Mauro Formica and Yakubu were matched by Marc Albrighton and Stiliyan Petrov as the game started with an open feel to it, but it was the visitors who grew with confidence and took charge of the first half.
After long spells of pressure the deadlock was eventually broken on 24 minutes. Villa centre back Carlos Cuellar given far too much space to advance down the left before cutting inside. Whether the Spaniard meant to shoot who knows but it teed up Charles N'Zogbia and the former Wigan man lashed the ball high past Paul Robinson into the roof of the net from 12 yards.
With Rovers struggling to gain any momentum going forward the visitors should have increased their lead. Stephen Ireland and Petrov both flashed wide, whilst Paul Robinson pulled off a superb save to deny N'Zogbia.
The last act of the first half was Rovers' best chance, a long throw into the area was flicked on at the near post by Grant Hanley it fell invitingly to Junior Hoilett but he hammered the ball over the bar.
Steve Kean made two changes at the break, Marcus Olsson, the older brother of Martin, making his home debut in replacing Radosav Petrovic. Whilst David Dunn was the second change with Mauro Formica making way.
Almost immediately the two Olsson's combined, Marcus setting Martin off down the flank, his centre was inches away from Yakubu who flung himself towards the ball in vain.
Villa went up the other end and very nearly extended their lead. Paul Robinson brilliantly getting down to his left to make a one-handed save from Stephen Ireland.
That chance aside it was then all Rovers in a thirty minute spell where they did everything but scored. Driven on by David Dunn Rovers were suddenly a different side, the pace of the two Olsson twins down the left also causing the visitors problems.
Steven Nzonzi fired narrowly over with a rasping drive before the Frenchman nodded Paul Robinson's free-kick down into the path of Scott Dann but the defender could only head onto the roof of the net.
A mazy run from Dunn followed, into the path of Hoilett but Given made the save. Moments later Given was at it again, alert to beat away a thunderbolt from Morten Gamst Pedersen.
With Rovers pressing and pressurising Villa made a double change. Barry Bannan and Gary Gardner on for goalscorer Charles N'Zogbia and Chris Herd.
But it was those who had been on from the start that almost brought an unlikely Villa goal, Warnock crossing for Agbonlahor to head goalwards only for Robinson to fling himself to save.
With five minutes to go the equaliser finally came. Having knocked on the door for so long the relief around the ground was palpable as Steven Nzonzi spread the ball wide to the right, Bradley Orr advanced in space to centre and the unlikely figure of David Dunn arrived at the back post to head down and into the back of the net.
The drama didn't end there as Aston Villa could have regained the lead, sub' Barry Bannan with a long-range effort that Robinson had to push behind.
Then at the other end in injury time Grant Hanley went close with a header from a Pedersen corner, the young Scot unable to get a clean connection as the ball flashed wide.
As Howard Webb blew the final whistle, Rovers will have been relieved to have grabbed a point, but will regret the missed chance to move out of the bottom three.
ROVERS: Robinson (c), Orr, Dann, Hanley, Martin Olsson, Pedersen, Nzonzi, Petrovic (sub Marcus Olsson 46 mins), Hoilett, Formica (sub Dunn 46 mins), Yakubu.
Subs: Bunn (GK), Modeste, Goodwillie, Vukcevic, Henley.
ASTON VILLA: Given, Hutton, Warnock, Collins, Ireland, N'Zogbia (sub Bannan 75 mins), Agbonlahor, Albrighton (sub Weimann 90 mins), Petrov (c), Cuellar, Herd (sub Gardner 75 mins).
Subs: Guzan (GK), Heskey, Lichaj, Baker.
Booked: Pedersen (Rovers).