With Los Cafeteros' World Cup opener against Greece just over three months away, coach Jose Pekerman gave a number of his fringe players the chance to shine as Christian Zapata, Fredy Guarin, Jackson Martinez all started on the bench.
Falcao's Monaco team-mate James Rodriguez opened the scoring from the penalty spot after Tunisian keeper Farouk Ben Mustapha had felled Victor Ibarbo after 20 minutes.
Tunisia responded well, though, and were level 15 minutes later when Wahbi Khazri drilled home Yassin Mikari's cross.
Colombia, who will also face Côte d'Ivoire and Japan in the group stages of the World Cup, had the lion's share of possession after the break.
However, without Falcao, who is struggling to make the World Cup after suffering knee ligament damage in January, and Martinez they didn't have the killer touch to turn their domination of the ball into goals.
Mustapha made amends for conceding the penalty when he saved bravely from Fiorentina's Juan Cuadrado.
Colombia were forced to see out the final ten minutes with ten men when Luis Perea saw a second yellow card for chopping down Fakhreddine Ben Youssef as he broke clear on goal.