With Ronaldinho having a quiet game in midfield, Tardelli scored one goal and laid on the added-time equaliser for Luan on the synthetic pitch at the Caliente in the Mexican border town.
Boca Juniors and Newell's Old Boys drew 0-0 in the first leg of their all-Argentine tie at La Bombonera in Buenos Aires.
Spindly striker Fidel Martinez put coach Antonio Mohamed's side two up in the 53rd minute when he tapped home after goalkeeper Victor dived to deflect Alfredo Moreno's stinging shot.
Tardelli warned Tijuana of what might come with a shot that goalkeeper Cirilo Saucedo deflected for a corner with his foot and pulled one back in the 66th at a corner with his sixth goal of South America's elite club competition.
Ronaldinho sent in his corner-kick close to the goal-line where a defender's effort to clear the ball at the near post merely lifted it past Saucedo to the far post where Tardelli volleyed in for the first goal conceded by Tijuana at home.
Argentine first division leaders Newell's came into their own more in the second half and Boca goalkeeper Agustin Orion had to make a diving save to push away striker Ignacio Scocco's scissored volley from Maxi Rodriguez's cross in the 69th.
