Holders Internacional also went on a goal spree in their 4-1 away win over Wilstermann in Bolivia but Santos, the third Brazilian side in action on Wednesday, lost 3-2 to Colo Colo in Chile having taken an early lead.
Twice champions Cruzeiro lead Group Seven with 10 points, four more than Estudiantes, the Argentine side that beat them in the 2009 final but whom they crushed 5-0 in their opening group match last month.
Tolima, who had held Cruzeiro to a 0-0 draw at home, had defender Julian Hurtado sent off four minutes from time for a second booking.
Internacional overcame the high altitude in Cochabamba to crush Wilstermann and go top of Group Six with seven points from three matches.
They lead on goal difference from Ecuador's Emelec, who beat Chiapas of Mexico 1-0 at home in Guayaquil, but have played a match less.
Inter settled the match in the opening 24 minutes after Wilstermann took an eighth-minute lead when their Argentine defender Juan Ignacio Brown headed home a free kick.
Brown then headed the Brazilian side's equaliser with an own goal trying to clear a cross and forwards Leandro Damiao and Ze Roberto put the game beyond Wilsterman with Kleber adding a late fourth.
In Santiago, Colo Colo went top of Group Five one point ahead of Paraguay's Cerro Porteno, who had beaten them 5-2 at home in their opening match. Santos are third with two points after all four teams have played three.
Midfielder Elano, recalled to the Brazil squad last week for the first time since the 2010 World Cup, put Santos ahead with a swerving free-kick that deceived Colo Colo's Uruguayan goalkeeper Juan Castillo.
The Chileans hit back with three goals in 17 minutes, the pick being the equaliser by Chile striker Esteban Paredes who chipped over keeper Rafael after taking a fine though ball from Argentine Ezequiel Miralles.
Teenager Neymar pulled one back for Santos, twice winners of the trophy in Pele's heyday in the 1960s, as the action flowed from end to end with near misses in both goalmouths.
Paraguay's Libertad became the first team to secure a berth in the knockout phase when Once Caldas were held 1-1 at home by San Luis of Mexico in Group One on Tuesday night in Colombia.
With two matches to go, Libertad are top of the group with 10 points, San Martin of Peru second with six, Caldas third with three and San Luis bottom on two.
The match in Manizales had a dramatic ending after Caldas had taken the lead in the 78th minute through full back Luis Nunez.
Fighting among players led to red cards for Caldas captain Alexis Henrique and San Luis defender Sergio Ponce in the 88th minute.
Then midfielder Juan Medina equalised in the fourth minute of added time leaving 2004 champions Caldas and San Luis with an uphill fight to secure the second qualifying berth.
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