Real Madrid defeated stubborn neighbour Leganes1-0 in the Copa del Rey quarter-finals first -leg on Thursday night at Estadio Butarque.
Real Madrid boss Zinedine Zidane made a number of changes with Cristiano Ronaldo, Gareth Bale, Sergio Ramos, Karim Benzema and Marcelo were all left out going to the encounter.
But after Leganes had shone on their first appearance at this stage of the competition, Asensio came up with a cute near-post finish from Theo Hernandez's cross to put Madrid in firm control of the tie.
Midfielder Mateo Kovacic missed a glorious chance in a quiet first-half as he latched onto a loose pass before shooting well wide of the Leganes goal.
Right-back Dani Carvajal went close with a driving volley across goal just before half-time but both teams continued to struggle in front of goal.
Leganes nearly scored when Marcos Llorente headed onto his own cross bar from a free-kick, before striker Claudio Beauvue was denied thanks to a fabulous save from Francisco Casilla.
Los Blancos looked to have run out of chances but Asensio scored with one minute remaining. Theo Hernandez charged down the left wing and crossed to the near post and Asensio was on hand to volley home past Nereo Champagne.
Real Madrid were poor for large parts of the contest, but Asensio's dramatic impact may serve to ease the growing pressure on Zidane ahead of Wednesday's return leg at the Santiago Bernabeu.