Bulgarian Dimitar Berbatov scored two goals and made another to propel Spurs into the Uefa Cup quarter-finals.
Berbatov has scored 19 goals this season
Having won in Portugal last week, Spurs had the worst possible start after Tom Huddlestone headed past Radek Cerny.
But Spurs were soon back in front as Berbatov scored with a right-footed flick and then a quite superb volley.
Andrade Joao Amaral's arrowed free-kick briefly threatened a shock, before Berbatov's pass freed Steed Malbranque, who flicked the ball past Paulo Jorge.
Spurs have now scored 23 times in seven games and Martin Jol's side gave their fans another three goals to savour.
The pick was Berbatov's breathtaking volley, though the passes that made the first and third goals were equally eye-catching.
Wednesday's victory also means Spurs have won all eight games they have played in the Uefa Cup this season as they bid to win the tournament they last won in 1984.
That outstanding record momentarily came under threat when Braga took a surprise lead after Huddlestone headed into his own goal following Amaral's curling free-kick.
Tottenham had dominated the game up to that point but even conceding that goal failed to dim Spurs' quixotic spirit.
If Berbatov's goals showcased his exquisite finishing skills, the Bulgarian was quick to credit the role played by first Robbie Keane and then Huddlestone in setting him up
Keane was surrounded by four Braga defenders but the Irishman's flick beat them all as Berbatov made a run to the left of his striking partner.
The pass deserved a goal and Berbatov did not disappoint, beating Jorge with a measured shot hit with the outside of his right foot.
Huddlestone had looked distraught after his own goal, but his demeanour improved immeasurably when his quick thinking from a free-kick provided the pass for Spurs' second goal.
Huddlestone's flighted pass was quickly chested down by Berbatov who swivelled to volley past Jorge with a stupendous strike.
Berbatov and Keane had chances to extend Spurs' lead before the interval, but neither striker was able to find the net.
Just before the hour Braga's hopes of pulling off a remarkable win were revived when Amaral thumped a free-kick past Cerny.
But for a third time in the game Braga had no answer to Berbatov, as the Bulgarian arced a pass over the Portuguese defence to find Malbranque who slipped the ball past Jorge.
Tottenham: Cerny, Stalteri, Dawson, Chimbonda, Young-Pyo Lee, Lennon (Ghaly 81), Huddlestone, Zokora, Malbranque, Keane (Defoe 66), Berbatov.
Subs Not Used: Alnwick, Tainio, Mido, Taarabt, Charlie Lee.
Booked: Berbatov, Malbranque.
Goals: Berbatov 28, 42, Malbranque 76.
Braga: Paulo Santos, Luis Filipe, Paulo Jorge, Rodriguez (Nem 40), Carlos Fernandes, Frechaut, Madrid, Joao Amaral, Joao Pinto (Cesinha 74), Ze Carlos (Maciel 74), Wender.
Subs Not Used: Dani Mallo, Castanheira, Ricardo Chaves, Bruno Gama.
Booked: Joao Amaral, Joao Pinto, Luis Filipe.
Goals: Huddlestone 24 og, Joao Amaral 61.
Ref: Laurent Duhamel (France).