The former West Ham, Newcastle United and Chelsea striker coolly tucked away a spot-kick in the closing stages, after Vlad Chiriches had handled, to ensure Slaven Bilic's side returned to Turkey with a point from this Group C encounter at White Hart Lane.
It was no more than Besiktas' display warranted, with Spurs goalkeeper Hugo Lloris twice denying Olcay Sahan with outstanding saves and also pulling off another excellent reaction stop to keep out Ba earlier in the piece.
Spurs moved ahead - somewhat against the run of play - through a well-taken goal from Harry Kane midway through the first half.
The 21-year-old striker, yet to start a Premier League game under Mauricio Pochettino, made it four goals in five appearances in cup competitions as he drilled home from outside the area.
However, Ba's subsequent leveller ensured a happier return to north London for Besiktas, after they were knocked out of the UEFA Champions League by Arsenal at the play-off stage in August.
Spurs have now won only one of their past seven matches in all competitions, and both they and Besiktas have two points from as many group fixtures.
Pochettino made 10 changes from Saturday's 1-1 draw at Arsenal with only Lloris keeping his place, and the goalkeeper survived a scare as early as the second minute when Sahan side-footed wide after capitalising on poor defensive play from Spurs.
Besiktas went even closer to opening the scoring 10 minutes later, Ba crashing a shot off the crossbar, and Gokhan Tore fired wide of the right-hand post midway through the half as the visitors made an assured start to proceedings.
Their positivity was punctured in the 27th minute, however, as Kane received a pass from Nabil Bentaleb and struck a sweet left-footed shot low into the bottom-right corner from 25 yards.
Lloris brilliantly denied Sahan six minutes later, somehow diverting the forward's close-range effort wide of the post with his trailing leg.
As the game opened up, Kane brought a save out of Tolga Zengin with a thumping effort from a tight angle.
Spurs began the second half brightly and Andros Townsend curled a shot off target from 20 yards after linking up well with Benjamin Stambouli.
Once again Lloris kept out Sahan, leaping high to his left to tip the ball over the bar after the Turkey international had been played in by Ba.
Bentaleb fired narrowly wide just before the hour mark, and Sahan's acrobatic volley flew wide of the upright in the 64th minute with Lloris motionless.
Kane was denied a second by a fine reaction stop from Zengin 19 minutes from time, before Besiktas substitute Mustafa Pektemek headed over with his first touch.
Lloris performed heroics again five minutes later to tip Ba's powerful effort from eight yards behind for a corner but, just when it seemed Tottenham would escape with a win, Chiriches needlessly handled under pressure from Pektemek and Ba stroked home the resulting penalty to rescue a draw.
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