In a battle of the two most successful clubs in Costa Rican league history, referee Randall Poveda dished out four yellow cards to each side before Heiner Mora scored the only goal of the game in the 91st minute.
Mora got on the end of a cross from the left wing to give Saprissa a crucial lead ahead of their semi-final second leg away to Alajuelense on Monday.
Saprissa - the most successful club in the Costa Rican Primera Divison - are aiming for their 31st championship but will have to be at their best next week when they travel to the Estadio Alejandro Morera Soto, as Alajuelense (29 titles) finished the Torneo de Invierno top of the table.
In the other semi-final first leg on Wednesday, Herediano triumphed 3-2 at Cartagines with both sides finishing the match with 10 players.
Kevin Vega struck in second-half stoppage time for Cartagines to give them some hope ahead of their trip to Heredia on Sunday but the Cartago-based club will have to do without Carlos Johnson, who received his marching orders in the 80th minute.
Just four minutes later, Herediano midfielder Francisco Calvo was also sent off.
Herediano started brilliantly with Yendrick Ruiz and Victor Nunez scoring in the seventh and ninth minutes, while the former added the visitors' third goal with eight minutes remaining.
Jameson Scott's penalty just past the hour mark got Cartagines on the board, before Vega's late intervention put them within a goal ahead of the second leg.
