Catolica, a goal up inside a minute through striker Lucas Pratto, fell 3-1 behind in the first half but fought back scoring twice in the dying minutes to win the Group Four match at the Argentine team's Fortin (fortress) stronghold in Buenos Aires.
"We made a good start and then made three mistakes despite playing well, but we kept going forward," Argentine man of the match Juan Eluchans told Fox Sports.
Catolica, coached by Argentine-born former Spain striker Juan Antonio Pizzi, went top of the group with four points from two matches, one point ahead of Velez and Caracas FC, who beat Chile's Union Espanola 2-0 at home.
Velez, South American champions in 1994, looked to have the match in the bag at half-time with solid defending and more organised attacks.
They equalised with a header by central defender Fernando Ortiz from a Maxi Moralez free kick after 20 minutes.
Midfielder Augusto Fernandez put Velez ahead two minutes later when he volleyed home playmaker Moralez's fine left cross and left-back Emiliano Papa headed their third in first-half added time.
TACTICAL ERROR
However, Velez coach Ricardo Gareca played the wrong cards after Ortiz was sent off in the 52nd minute for a second booking, sending on defender Fernando Tobio and taking off Moralez, who did not look happy about the change.
Velez retreated, handing the initiative to Catolica who ended up running the Argentine side into the ground with their speedy breaks down the flanks, notably on the left where wing-back Eluchans was inspirational, and diagonal runs across the defence.
A 74th minute goal by midfielder Tomas Costa put Catolica, finalists in 1993, back in the match.
Eluchans attacked on the left and threaded the ball through to Costa who scored with a shot from outside the box that went in close to goalkeeper Marcelo Barovero's far post.
With less than two minutes remaining Argentine Pratto equalised, swivelling in the box to hit a left-footed shot that went in after hitting both posts.
A Velez attack broke down on the edge of the box in added time and Catolica raced down the other end where Argentine Marcelo Canete, on loan from Boca Juniors, laid the ball off to the right for fellow substitute Francisco Pizarro to brilliantly chip it over the advancing Barovero for the winner.
LDU Quito, who won the title in 2008, beat record seven times champions Independiente of Argentina 3-0 at home in the Ecuadorean capital to leave all four teams in Group Eight on three points from two games.
