Dimitar Berbatov opened the scoring early on with his 14th league goal of the campaign as Tottenham dominated from the off.
But Morten Gamst Pedersen fired the home side level on the half-hour mark after a well-worked team move.
Rovers, who have now lost just two of their last 15 league games, had late a penalty claim turned down when David Bentley appeared to have his run blocked in the box.
Rovers boss Mark Hughes made two changes to the side that drew 0-0 away to Reading last time out. New signing Johann Vogel was handed his debut in place of the injured David Dunn, while Chris Samba returned from suspension at the expense of Zurab Khizanishvili.
Juande Ramos made four changes to the Spurs side that were humbled 4-1 at home to Newcastle, with Radek Cerny, Pascal Chimbonda, Jermaine Jenas and Aaron Lennon coming in for Paul Robinson, Jamie O'Hara, Tom Huddlestone and Darren Bent.
Both sides looked lively in the opening exchanges, but it was the visitors that took the early lead. On seven minutes, Steed Malbranque cut open the Rovers defence with a throughball to Jenas, who centred for Berbatov to stab home from two yards.
The same two players almost combined again seven minutes later, but Berbatov was just unable to collect Jenas' precise pass.
The Rovers rearguard were all at sea, as Spurs split them wide open once again. Chimbonda played the pass on this occasion, but Brad Friedel made an excellent block to deny Berbatov.
But against the run of play, Rovers restored parity with a terrific team goal. With a third of the game gone, Steven Reid spread the play wide to Bentley.
The England man's first touch took him past Chimbonda and, with bodies to pick out in the centre, he pulled the ball back to Pedersen, who coolly side-footed the ball into the corner of the net.
Less than a minute later and another good Rovers move ended with Roque Santa Cruz firing a left-foot shot straight at Cerny in the Spurs goal.
Rovers ended the half much stronger than they had started it and they could have taken a lead into the break had Bentley's top corner-bound free-kick not been saved.
In an exciting opening to the second half, Berbatov volleyed straight at Friedel at one end, while Vogel volleyed over the bar at the other.
A minute later, Jason Roberts' low drive was comfortably dealt with by Cerny, before Friedel made a double save, first from Malbranque and then from Lennon.
As the minutes ticked by, both managers rang the changes and it was one of the Spurs substitutes who almost cost his side the game.
On 81 minutes, Bentley's surging run into the box was brought to a halt by Gilberto, but referee Peter Walton waved the strong penalty appeals away.
Bentley then had a free-kick saved at one end, while Jenas suffered the same fate at the other, as both sides had to settle for a share of the spoils.