Hossam Ghaly, who won the spot-kick for the visiting side, was also dismissed for a late elbow on Michael Gray as Rovers ended their four-game losing streak.
Rovers boss Mark Hughes made three changes to the side that lost 1-0 to Premiership leaders Manchester United at Ewood last weekend.
Defensive duo Lucas Neill and Zurab Khizanishvili missed out through injury and suspension respectively, while Robbie Savage returned from a two-game lay-off in place of Aaron Mokoena.
Stephane Henchoz was handed his first league start following his return to the club, while Gray was preferred at left-back.
Spurs manager Martin Jol made four changes following last Sunday's surprise 3-1 defeat away to Reading.
Defoe and Mido, who almost joined Rovers in the summer, started in place of Robbie Keane and Dimitar Berbatov in attack, while Edgar Davids and Tom Huddlestone came in for injured England duo Jermaine Jenas and Aaron Lennon.
After a slow start, Rovers thought they had taken the lead with their first attack of the game.
On seven minutes Henchoz found Benni McCarthy down the line, the South African's extravagant flick fell perfectly for David Bentley and the former Arsenal man slipped in Shabani Nonda who finished well only to be flagged for offside.
Davids registered Spurs' first effort at goal with a low drive, before Rovers took the lead in sensational circumstances midway through the first half.
Amid half-hearted appeals for a penalty, Morten Gamst Pedersen headed Gray's ball back across goal, Ledley King rose to clear, but Tugay was on hand to strike a sublime first-time volley into the top right-hand corner of the net from 25 yards.
The visitors responded well with Defoe going close on two separate occasions.
On 33 minutes he spun past Henchoz before forcing Brad Friedel to punch clear and just three minutes later he reacted quickly in the box before fizzing a right-foot volley just inches over the bar.
Mido threatened twice in stoppage time at the end of the first half, before almost drawing the sides level just two minutes after the break.
After a foul by Brett Emerton, Huddlestone delivered an in-swinging free-kick from the left, Mido stole in to glance the ball into the far corner with a deft header but again the linesman on the near side raised his flag.
The officials were called into action again on the hour-mark with the talking point of the game.
Ghaly broke through the centre before flicking the ball over Tugay inside the box. When the Egyptian hit the deck, Tugay was adjudged to have brought him down and was sent off for being the last man.
Defoe stepped up and although Friedel dived the right way, the England man just squeezed the ball past him into the bottom left-hand corner of the goal.
Two minutes later Rovers thought they should have had a penalty of their own.
Savage's free-kick sailed just over the head of captain Andre Ooijer, but Mido appeared to control the ball with his arm, only for referee Phil Dowd to wave play on.
McCarthy's back-heel flick from Gray's near-post cross forced Paul Robinson into a smart reaction save, before both Ghaly and Jol were sent to the stands with the elbow incident three minutes into time added on.