'Los Cafeteros' went into the game third in the group and until almost the hour mark it looked to be them that would be eliminated, only for their goal and Poland's winner against Japan to turn the group on its head.
Senegal started the better side in Samara, constantly probing and pressing with their pace and direct running.
Despite that it was Colombia who had the game's first real effort, Juan Quintero forcing a save from Khadim N'Diaye with a low free-kick.
Nevertheless Senegal continued in the same vein. Sadio Mane was at the heart of all their best stuff and he looked to have earned his side a penalty with 15 minutes on clock when his marauding run was ended abruptly by Davinson Sanchez.
The referee immediately pointed to the spot, only to overturn his decision having viewed the incident again on the pitchside monitors.
Keita Balde was handed his first start of the tournament, but a curling effort that flew straight into the arms of David Ospina with 27 minutes gone was his only real contribution.
Colombia suffered a hammer blow on the half-hour mark as talisman James Rodriguez was forced off through injury, but they managed to battle through to half-time with the scores level.
- Second half turnaround -
Colombia started better after the interval, but it was a goal in the other game in the group that finally sparked some life into the day's games as Jan Bednarek put Poland ahead against Japan.
That meant that both Colombia and Senegal would progress, though the South Americans appeared keen to secure passage off their own backs as they threatened through substitute Luis Muriel and Falcao.
With just 16 minutes to go the deadlock was finally broken and it came from an unusual source, Yerry Mina rising highest to meet Juan Quintero's corner from the right and power home his second goal of the tournament to send Colombia top of the group.
Now trailing to Japan on yellow cards, Senegal had no option but to throw men forward in seearch of a goal. However, despite Mbaye Niang and Ismaily Sarr both trying their luck they were left frustrated as Colombia held out to top group H, with Japan joining them in the last 16.
Colombia will now face whoever finishes second out of England and Belgium in Group G, with Japan facing the group winners.