We led 1-0 via Ruben Lamieras' fine strike on 39 minutes when what had been a game of few chances burst into life.
Rovers' substitute Dean Rittenburg levelled at 1-1 on 82 minutes only for us to re-take the lead two minutes later through Shaq Coulthirst.
Our joy was short-lived, however, as Bryan Dabo finished from close range for 2-2 four minutes from time.
We were inches away from a winner when Darren McQueen hooked a volley just wide in the final minute.
A young team took to the impressive set-up at Leigh to take on a Rovers side that included Lucas Neill, the former Millwall, Blackburn and West Ham defender capped 96 times by Australia.
The first chance arrived on seven minutes when Coulthirst floated a pass wide to Kenny McEvoy and his low cross looked destined for Souleymane Coulibaly, only for Ryan Edwards to touch it away from the striker in front of goal.
Alex McQueen did well to clear from Deniz Pero on 17 minutes and play switched straight up the other end, Coulthirst forcing the first save of the match from David Raya.
Both teams continued to work their way into promising positions with no reward, but we slowly started to take control territorially, with Lameiras the link man, drifting everywhere off the front men.
Jordan Archer made a comfortable save from Dabo on 37 minutes and we struck the opener two minutes later.
Coulthirst was brought down in the left channel, Milos Veljkovic curled in the free-kick that was cleared out to Aaron McEneff, his shot fell to Lameiras who needed no second invitation, dispatching a low shot home off the post from 20 yards.
Coulibaly almost doubled the lead on 45 minutes, his free-kick up and over the wall from 22 yards but clipping the top of the crossbar.
The second half followed a similar pattern to the first as we edged it territorially, but Rovers proved a tough nut to crack, marshalled by Neill.
The home team had a couple of decent efforts from distance from Dabo and Pero, who drilled just over and then stung Archer's hands from 25 yards.
Lameiras went close again from a free-kick on 69 minutes, a left-foot strike from a central position that beat the wall and zipped just past the post.
It looked like we might hold on for a 1-0 win but two of Rovers' substitutes combined to level the scores with eight minutes left, Will Beesley releasing Rittenburg, who finished one-on-one past the advancing Archer.
We were soon back in front though as Laste Dombaxe, on 10 minutes earlier for McEneff, whipped in a free-kick to the near post area, turned home by Coulthirst.
But Blackburn hit back again in the 86th minute as Mahoney delivered a free-kick from the right, Edwards nodded back into the danger area and Dabo buried from close range.
There was one more chance as Darren McQueen latched onto McEvoy's cross in the 90th minute and managed to hook a volley towards goal, the ball arcing across Raya almost in slow motion before landing inches wide.
Rovers: Raya, Fernandez Molina, Tumwa, Evans (Cotton, 62), Edwards, Neill, Mahoney, Lenihan, Pero (Rittenburg, 67), Dabo, Bauress (Beesley, 62). Unused subs: Urwin, Preston.
Spurs: Archer; A McQueen, Ball, Gallifuoco, Stewart; Lameiras (Sonupe, 83), McEneff (Dombaxe, 72), Veljkovic; Coulibaly (D McQueen, 83), Coulthirst, McEvoy. Unused sub: McGee.