With no extra time, penalties were needed after Luis Diaz equalised in the 61st-minute to cancel out Lautaro Martinez's first-half opener in Brasilia on Wednesday (AEST).
Emiliano Martinez was the hero in the shoot-out after the Argentina goalkeeper saved three spot-kicks to send the 14-time Copa winners – eyeing their first major title since 1993 – through to Sunday's blockbuster decider against defending champions Brazil.
Messi, who is craving his first senior crown with La Albiceleste, was brilliant from the outset, the superstar dancing past three players before picking out Lautaro Martinez, but the latter's header sailed just wide of the post in the fourth minute.
Martinez got his goal three minutes later, however, after drilling home past David Ospina – Messi with the presence of mind to twist away from Yerry Mina before lifting his head and finding the Inter star.
Colombia almost celebrated an immediate response, though Emiliano Martinez was on hand to deny Juan Cuadrado – earning his 100th cap – just moments later.
As has so often been the case during the tournament, Argentina fell away following a bright start and Colombia were unfortunate not to equalise.
Colombia came within a whisker of restoring parity in the 37th minute, hitting the woodwork twice within seconds after Mina's header rattled the crossbar from the resulting corner following Wilmar Barrios' deflected shot that struck the post.
On the stroke of half-time, Argentina went close to doubling their lead after Nicolas Gonzalez's header was narrowly pushed onto the roof of the net by Ospina.
Colombia responded well to falling behind and they were eventually rewarded via Diaz's equaliser just past the hour-mark.
Diaz got in behind Argentina's defence following a quick free-kick and the winger somehow managed to beat Emiliano Martinez from an acute angle as Lionel Scaloni's men were caught napping.
Colombia were fortunate to still be on level terms when Ospina came flying out of his penalty area as substitute Angel Di Maria charged through, but Barrios was on hand to make the last-ditch goal-line block, denying Lautaro Martinez in the 73rd minute.
Messi then saw his shot hit the woodwork with nine minutes remaining during a tense finale as the showdown headed to penalties.