The 22-year-old, who has attracted criticism this season, returned to the United starting line-up after missing Saturday’s win over Bristol City through injury.
And the Northern Ireland international got the home fans back on his side with a stunning save at the death to deny Marc McNulty.
With Leeds 1-0 ahead following Stuart Dallas’ 60th-minute strike, the Royals were given a lifeline when Barry Douglas brought down Josh Sims in the area.
But Peacock-Farrell proved to be the hero, diving to his right to turn behind McNulty’s low effort from the spot, as Leeds moved into second place in the Championship.
“I’m very happy for him and I’m very happy for the team,” Bielsa said. “We had an intervention which resolved the game. He has a very big influence.”
Similar to the Bristol City game at the weekend, Leeds were struggling to break Reading down.
Bielsa took matters into his own hands at half-time, injecting pace and creativity into his side with the introductions of Samuel Saiz and Jack Clarke for Gjanni Alioski and Lewis Baker.
That improved Leeds and their pressure finally paid off when Dallas, again playing as a makeshift right-back, converted from close range on the hour.
On the double substitution, Bielsa said: “We had more offensive fluidity (in the second half), especially at the beginning.
“Their contribution was important. Our performance had ups and downs, we were not that regular but generally speaking we deserved to win.”