The Africans had six yellow cards at the tournament while Japan had four yellow cards.
It was an emphatic reaffirmation of their potential after 10-man Colombia, quarter-finalists in Brazil four years ago, had suffered an upset defeat in their opening game to Japan.
Senegal remains Africa's only hope for a place in the next round but face an uphill task in an overcoming a Colombia team that is n the ascendancy and also have their key player - James Rodriguez peaking at the most crucial time.
Colombia play the runner-up from Group G, either England or Belgium, in Moscow on Tuesday with Japan facing the Group G winners the previous day in Rostov-on-Don.
But Yerry Mina's late goal gave the South Americans victory and left Senegal and Japan level on points, goal difference and head-to-head.
The likes of Falcao and Juan Cuadrado underlined the quality in a team that welcomed back James Rodriguez, top scorer at the last World Cup, to a leading role after starting him from the bench against Japan.
Colombia is the only team in Russian Federation to lose its opener - 2-1 to Japan - and make it to the round of 16.
Yet Mina ensured Colombia were not made to pay when he headed home in the 74th minute.
Both teams were on track to move into the knockout stages with 16 minutes remaining in Thursday's clash at the Samara Arena, due to Japan trailing 1-0 to Poland in Volgograd.
Carlos Sanchez returned to the Colombia line-up after suspension.
Mina, 6-foot-5, leapt above a pair of Senegalese defenders to head the ball hard off the ground and off Senegal goalkeeper Khadim Ndiaye's hand, sending the enthusiastic Colombian fans at Samara Stadium into a frenzy. Sanchez received criticisms and a death threat, which is being investigated by Colombian authorities.
Senegal lost a World Cup group-stage game for the first time in their history.