Jose Pekerman's men were all over their west African opponents in the first half of their friendly, and converted their dominance by taking a 2-0 lead into the interval courtesy of goals to Carlos Bacca and Teofilo Gutierrez.
Senegal's response was emphatic, as they equalised within seven minutes of the restart via goals to Moussa Konate and Cheikh Ndoye - the latter a stunner from range.
Alain Giresse's men had to battle for 24 minutes a man down, though, as midfielder Ibrahima Seck was sent off for picking up a second yellow card.
But despite their numerical advantage, Colombia could not capitalise as they slumped to their third straight stalemate in preparation for their Group C campaign at the FIFA World Cup in Brazil.
Among those starting for Colombia was wing-back Camilo Zuniga, who had just 49 minutes for Serie A side Napoli since knee surgery in October.
Bacca's back-post header from a Colombia corner found Gutierrez right in the goalmouth in the 11th minute, and he had an easy tap-in to convert their early dominance of possession.
There was more danger for the west African nation moments later, with midfielder Seck conceding a foul on Zuniga on the edge of the area, however, Juan Quintero's effort bounced wide of the target.
Colombia were looking dangerous on the counter-attack, with multiple Senegal corners turning into forays forward for the South American nation.
And Colombia would double their lead just prior to half-time, when Victor Ibarbo got on the end of a long ball, centred a pass for Bacca, who lashed home an effort high into the net to send them into the break with all the momentum.
Senegal had a couple of shots from range in the final 10 minutes of the half, but none that had Colombia custodian Faryd Mondragon too concerned.
However, the African side would be level just seven minutes into the second half, after a barrage on Colombia's defence.
Pekerman made four half-time substitutions - one of which being Zuniga - and it seemed to unsettle the fifth-ranked nation.
Konate made Colombia pay for a turnover in their defensive half, as he ran onto Mohamed Daf's through ball to calmly slot the ball past Mondragon's left hand.
That was followed by Ndoye's thumping effort from outside the area, with his 52nd-minute shot giving Mondragon no chance.
Senegal were all over the World Cup-bound Colombians, and Zargo Toure almost put them ahead - only denied by a diving Mondragon, who parried to safety.
Giresse's men were down to 10, though, when Seck received a second yellow for a raised foot on second-half substitute Alexander Meija.
Quintero's 74th-minute free-kick went over the bar, as Colombia pressed for a winner.
Sub Jackson Martinez - who came on for Bacca on 66 minutes - saw his shot deflected wide for a corner in the 77th minute, although the corner from Santiago Arias - who was looking dangerous out on the right - amounted to nothing.
And despite a flurry of possession late, the Colombians could not break down the Senegalese defence.
