Karim Benzema netted twice and Gareth Bale scored a trademark goal as Real Madrid overcame an early scare at Girona to win 4-1.
Asensio won his side's second spot kick as Pere Pons lunged at the Real forward.
This time it was Karim Benzema who stepped up to stroke home the penalty for his first goal of the season.
Bale produced a typical finish for Real's third goal, sprinting away from the Girona defence after being released by a wonderful pass from Isco and calmly steering the ball home.
Benzema scored his second on 80 minutes as he collected Bale's tempting cross and had time to turn and power the ball home.
The referee referred the goal to VAR for suspected offside but the goal was allowed to stand.