The winners of the quarter-final tie will meet Brazilian champions Fluminense or Olimpia of Paraguay, who are locked at 0-0 after their first leg in Rio de Janeiro.
Santa Fe's victory in the former Inca city of Cusco was their second win over Garcilaso in the competition after a home victory in the group phase.
Teams visiting Cusco usually have trouble with the thin Andean air at 3,600 metres above sea level but Santa Fe are not so disadvantaged being based in Bogota, which is only 1,100 metres lower.
In a match highlighted by constant end-to-end action in which Garcilaso paid for defensive frailties, defender Francisco Meza put the visiting side ahead in the 21st minute when he met a low cross with a left-foot volley.
Santa Fe went two-up three minutes later with a goal by striker Wilder Medina from a neat back-heeled pass on the edge of the box that tore the home defence apart.
Garcilaso missed a penalty two minutes later after a handball by defender Yulian Anchico, midfielder Fabio Ramos blasting his spot kick over the bar.
Striker Jefferson Cuero made it 3-0 for Santa Fe early in the second half before Argentine Alfredo Ramua pulled one back for the Peruvian side with a 25-metre drive into the top corner.
Garcilaso could have gone ahead as early as the 12th minute but striker Mauricio Montes, who hit the woodwork three times in the first half, was foiled by the post.
"At some point... in a demanding tournament like the Libertadores Cup, we were going to pay dearly for a lack of grade and character one gets with championships and (many) matches," Garcilaso coach Freddy Garcia said.
Garcilaso are a young club formed in 2009 and playing in South America's elite club competition for the first time.
The match at the San Januario in Rio was played in a downpour with Fluminense camped most of the time in the Olimpia half but unable to score thanks to dogged Paraguayan defending and a fine performance from Uruguayan goalkeeper Martin Silva.
"This wasn't what we expected (but) at least the advantage of a scoring draw will be ours," Fluminense captain Fred said looking ahead to next week's second leg away in Asuncion.
"Unfortunately we didn't score the goals to win, we created (chances) but were slack with the penultimate ball," the Brazil striker said.
Silva saved from defender Leandro Euzebio, midfielder Jean and striker Rafael Sobis and was lucky when midfielder Rhaymer scuffed his shot after rounding the keeper.
Olimpia midfielder Eduardo Aranda was sent off seven minutes from time for a second yellow card for one of a string of niggling fouls that helped the three times South American champions get the draw they celebrated like a win.