The build-up to the Sky Bet Championship fixture was dominated by Derby's claim that a Leeds employee was escorted from the perimeter of their training complex by police on Thursday after "acting suspiciously".
Bielsa accepted responsibility for the incident in a pre-match interview, although he insisted he had done nothing illegal.
The United head coach could face action from the Football Association but he would have been delighted with his side's response on the field as they beat Derby comfortably for the second time this season.
Kemar Roofe scored his 14th goal of the campaign to give Leeds a deserved half-time lead and the hosts secured three welcome points just after the restart thanks to Jack Harrison's tap-in.
The result ended Leeds' three-match losing run and stretched their lead at the top to five points, denting Derby's hopes of catching the top two in the process.
Home fans chanted "All spies aren't we" and "We're Leeds United, we'll spy where we want" as the players lined up in the tunnel and the raucous atmosphere continued in an eventful opening.
Leeds appeared to have made a dream start inside the first minute when referee Andy Davies awarded a penalty after Ezgjan Alioski had been bundled over in the box, only to see his assistant had incorrectly flagged for offside.
United continued to pile on the pressure and somehow failed to take the lead as returning captain Liam Cooper scooped Pablo Hernandez's corner over the bar from two yards out.
It was no surprise when the goal came on 20 minutes, exciting youngster Jack Clarke gliding past Craig Bryson before sending over a cross which was guided home at the near post by Roofe.
Clarke himself dragged a shot wide and Harrison had a tame header comfortably saved by Scott Carson as Leeds sought a second goal.
Derby's first effort came after 34 minutes when Tom Lawrence found some space midway inside the Leeds half, only to blaze harmlessly over from 25 yards.
United quickly reasserted control with the impressive Adam Forshaw fizzing a long-range strike just wide and tensions threatened to boil over on the stroke of half-time when Pontus Jansson was scythed down.
Derby, missing the influential Harry Wilson, introduced the experienced David Nugent in place of right-back Andre Wisdom at the break in a bid to turn the tide.
But the visitors were left with an improbable task just a minute into the second period when Carson could only parry Clarke's floated cross and Alioski's scuffed centre left Harrison with a gift.
Nugent was presented with an unexpected opportunity to get Derby right back in it when Bailey Peacock-Farrell came charging out of his goal and only just managed to block the striker's 40-yard attempt with his legs.
Derby went on to enjoy their best spell of the game but Leeds remained a threat on the break and twice went close through substitute Jamie Shackleton and the irrepressible Clarke.
The teenage winger was given a standing ovation as he was substituted and Leeds comfortably played out the final 10 minutes to record a much-needed win.