The Monaco striker is doubtful for the FIFA World Cup in Brazil due to a knee injury and he watched on from the stands at Espanyol's Cornella-El Prat Stadium in a friendly that gave his potential replacements - if he is ruled out - a chance to stake their claim.
Falcao's club-mate James Rodriguez handed the side ranked fifth in the world the lead from the penalty spot after Victor Ibarbo had been brought down by Tunisia goalkeeper Farouk Ben Mustapha.
That challenge resulted in Ibarbo being replaced with what appeared to be a back injury and Tunisia equalised in the first half when Bastia striker Wahbi Khazri took advantage of a mistake from keeper David Ospina to finish clinically.
Defender Luis Amaranto Perea saw red following a second bookable offence nine minutes from time for Colombia, who still could have won it late on through Adrian Ramos, making his first international appearance in two years. However, Tunisia were good value for a draw that raised morale after they failed to qualify for the World Cup.
Colombia coach Jose Pekerman gave Sevilla striker Carlos Bacca and Cagliari's Ibarbo a start, with Teofilo Gutierrez dropping to the bench.
The South American nation started brightly and were in front after 20 minutes, Rodriguez calmly slotting home the spot after Ibarbo was clattered by Ben Mustapha.
The unfortunate Ibarbo was unable to continue as a result of that incident and so on came Ramos to make his international return.
Tunisia responded and Ospina had to be alert to deny Issam Jemaa 22 minutes in, before Yassin Mikari also forced a save from the Colombia keeper.
Ospina had a moment to forget 10 minutes before half-time, though, as he flapped at a high cross from Mikari and Khazri was on hand to punish him with a well-executed lob.
The keeper was taken off at the break, with veteran stopper Faryd Mondragon replacing him, and Abel Aguilar also entered the fray along with Gutierrez at the expense of Mario Yepes and Bacca.
Rodriguez was brought down in full flow and fired the resulting free-kick wide early in the second half.
Juan Cuadrado was then denied by Ben Mustapha at his near post after 69 minutes as Colombia went in search of a winner.
Perea was given his marching orders for a second caution but Ramos almost snatched the win for Colombia, only to fire wide after being played through by Rodriguez.
