La Russa, manager of the St. Louis Cardinals, is third in career regular-season wins. Cox ranks fourth.
Cox is retiring after the season. Barring a playoff matchup, Sunday night's game was the last time La Russa will manage against Cox.
La Russa said Sunday he asked Cox to sign a lineup card and a baseball. The autographed ball sat on La Russa's desk before the game.
"It's special," La Russa said.
The history between the two managers could almost fill a season. Cox entered Sunday night's game 94-66 in 160 regular-season games against La Russa.
The managers split two playoff series. The Braves beat La Russa's Cardinals in the 1996 NL championship series. St. Louis swept three division series games against Atlanta in 2000.
La Russa is 6-4 against Cox in postseason games, all between the Cardinals and Braves.
"I feel like I've known Tony my whole life," Cox said.