With half an hour gone at a packed Monumental on Sunday, midfielder Ariel Rojas crossed from the left and Trezeguet met the ball with a first-time shot that hit the ground and bounced over goalkeeper Agustin Silva into the net.
"It wasn't the perfect match but there was a lot of enthusiasm from the players, it was a deserved victory," Trezeguet told reporters.
"It's a great personal satisfaction to score again at the Monumental and in front of this great crowd," the former France striker added after his first league goal since September.
Lanus took their tally to seven goals in two matches when they crushed crushed Newell's Old Boys 3-0 away in Rosario.
River's arch rivals Boca Juniors, licking the wounds of a shock home defeat by Mexico's Toluca in a midweek Libertadores Cup match, drew 0-0 at Tigre.
Boca, Tigre and Godoy Cruz, who beat Union 2-1 in Mendoza on Saturday, have four points.
Independiente, who had right-back Julian Velezquez sent off for a second booking in the 21st minute, stunned title holders Velez Sarsfield 1-0 away on Saturday thanks to central defender Cristian Tula's goal on the stroke of half-time.
The win boosted a Red Devils side tormented by the threat of relegation while for 'Inicial' championship winners Velez it was a second defeat in succession after losing away to Ecuador's Emelec in the Libertadores Cup last week.
