Spurs tightened their grip on fourth place after securing a thrilling win.
Keane has scored 10 goals in the league this season
Robbie Keane scored twice in the opening half, first with a superb effort after a contentious throw-in and then with a close-range finish.
Blackburn argued Keane's second should have been disallowed for handball but on 43 minutes Florent Sinama Pongolle's header reduced the deficit to 2-1.
On 70 minutes Bellamy drilled home the ball to level the scores but then Mido turned in Aaron Lennon's cross.
The win moved Spurs five points clear of fifth-placed Arsenal and six ahead of Blackburn, who are also chasing a European place.
Blackburn were probably unlucky not to claim at least a point, given the nature of Keane's goals and the visitors' domination of possession.
In the 90th minute Michael Gray hit the Spurs bar with a looping header as Blackburn desperately searched for that third goal to square the game.
Keane's first goal was a wonder to behold, even though it stemmed from a throw-in that should have been awarded to Blackburn.
Television replays clearly showed the ball touched Mido before it went out but instead the throw was given to Spurs.
The Eygptian quickly took the throw, picking out Keane, who - with his back to goal as well as being closely marked by Robbie Savage - still had plenty to do.
Despite that unpromising position, Keane nonchalantly flicked the ball over Savage, slipped inside Andy Todd with a second, sharp piece of skill, before hammering a shot past keeper Brad Friedel.
Having fallen behind to that goal, Blackburn mounted a spirited comeback, dominating possession, if struggling to create clear opportunities.
Just past the half-hour Blackburn did contrive to produce a gilt-edged chance only for Pongolle to miss badly.
With the goal at his mercy the on-loan Liverpool striker failed to prod home the ball following Ryan Nelsen's header.
Nelsen's next contribution proved rather less helpful when his deliberate handball gave away a free-kick on the edge of the Blackburn penalty area.
Mido guided his shot round the Blackburn wall with such power that Friedel was only able to touch the ball into Keane's path - or arm as the visitors claimed - and the Irishman made no mistake with a close-range finish.
While Keane was tying up Blackburn in knots, at the opposite end Spurs found Bellamy equally troublesome.
Two minutes after Keane's second, Bellamy scampered down the wing and sent in an inviting cross for Pongolle, whose diving header marked his first goal for Blackburn.
After the interval Blackburn continued to have the better of proceedings and Paul Robinson showed great agility to turn over David Bentley's rising shot.
Blackburn drew level when Pongolle latched on to Ledley King's poor header and crossed for Bellamy, who swept a half-volley past Robinson.
Having worked so hard to get back in the game Blackburn let their guard down three minutes later, allowing Lennon to cross for Mido, who touched the ball into the empty net.
Tottenham: Robinson, Stalteri, Dawson, King, Lee, Jenas, Carrick, Davids (Lennon 59), Tainio (Murphy 77), Mido, Keane.
Subs Not Used: Cerny, Defoe, Davenport.
Booked: Lee, Mido.
Goals: Keane 9, 42, Mido 70.
Blackburn: Friedel, Neill, Todd, Nelsen, Gray, Emerton (Kuqi 83), Reid, Savage, Bentley, Bellamy, Sinama Pongolle.
Subs Not Used: Enckelman, Dickov, Mokoena, Peter.
Booked: Gray, Reid, Todd.
Goals: Sinama Pongolle 44, Bellamy 67.
Ref: H Webb (S Yorkshire).