The Borussia Dortmund striker finished off a well-crafted move involving Juan Cuadrado and James Rodriguez shortly before the interval as Jose Pekerman's side prevailed in Ljubljana.
After being played in by Rodriguez's pass, Ramos coolly rounded goalkeeper Jan Oblak and tapped home his third international goal.
On a bobbly playing surface, Colombia managed to knock the ball around in typically attractive style, with captain Rodriguez to the fore.
The Real Madrid man was replaced 17 minutes from the end as Pekerman utilised his options from the bench, and Colombia held on as Slovenia were unable to force a late equaliser.
Defeat means Srecko Katanec's men have now lost each of their last four friendlies, without scoring a goal.
The hosts changed their entire starting XI from Saturday's 3-1 Euro 2016 qualifying defeat to England and went close early on as Nejc Pecnik fired narrowly wide from 20 yards in the third minute.
Colombia looked the more likely, though, with Rodriguez and Cuadrado linking up well with the front pairing of Ramos and Jackson Martinez, who replaced Teofilo Gutierrez and Carlos Bacca - the goalscorers from Friday's 2-1 win over the United States.
The home side did pose a threat on the break and Dejan Lazarevic curled an effort wide of the right-hand post eight minutes before the interval.
Ramos broke the deadlock six minutes later, however, as quick thinking from Cuadrado and Rodriguez at a free-kick helped to play in the striker, who took the ball past Oblak and tucked into an empty net.
Slovenia made four changes at half-time and one of those, Jasmin Kurtic, had Camilo Vargas scrambling across his line with a bouncing shot from 35 yards.
Substitute Damjan Bohar stabbed an effort wide of goal from close range as Slovenia pushed for a leveller, but one was not forthcoming as the visitors emerged victorious from the first meeting between these two sides.
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