Copa Libertadores Wrap: Cristal claim crucial win
Lobaton netted either side of Brian Fernandez's 67th-minute effort at the Estadio Presidente Juan Domingo Peron.
Despite the loss, Argentina's Racing (six points) remain on top of the group - ahead of Sporting (five) and Guarani (four).
Sporting went ahead away from home in the 58th minute.
Irven Avila did the hard work down the right, drawing out goalkeeper Sebastian Saja before cutting back for Lobaton to side-foot home.
A clever set-piece routine led to Racing's equaliser, with Fernandez on the end of it and driving into the roof of the net from inside the area.
A penalty decision went Sporting Cristal's way and Lobaton put his spot-kick straight down the middle to score the 81st-minute winner.
In the group's other game, Guarani eased past Deportivo Tachira 5-2.
Three goals in seven first-half minutes proved decisive for the Paraguayans, as Jorge Mendoza, Federico Santander and Julian Benitez scored.
Both teams finished the clash with 10 men.
Group Five's second-placed team, Wanderers, edged Palestino 1-0 thanks to a Matias Santos goal.
Group Three leaders Club Universitario were held to a 0-0 draw at home to Huracan.