After Mateusz Klich put Leeds ahead on the stroke of half-time, Leeds overran Burnley in the second half, with Jack Harrison doubling their lead before getting the assists on substitute Rodrigo's late brace.
Bielsa's side turned on the style the longer the game went on, with Rodrigo's introduction just before the hour a key moment as the Spain forward added a third with a fine piece of skill before capping a sweeping team move by rounding Bailey Peacock-Farrell to finish.
"In the first half we insisted until we managed to score," Bielsa said.
"We defended well. In the second half we didn't defend as well, but we were efficient and we had chances at goal.
"When there are big spaces, it is easier to attack. When the opponent is losing they take more risks.
"As you can also see, we conceded chances in the second half that we didn't in the first.
"The goals are all beautiful – don't think we scored them because we trained them."
Amid Leeds' fine play after the break, there was one ugly flashpoint at 2-0 with around 20 minutes left.
When Ezgjan Alioski went down under a challenge from Dwight McNeil, the Burnley winger appeared to say something to the North Macedonia international while he was on the ground before the Leeds man got to his feet and responded by sticking his tongue out and cupping his ears.
Both benches got involved in the argument unfolding before them, and referee Graham Scott called over both captains and managers after a report was made to him by a Burnley player.
"A report has come into the referee and that will be passed on to the FA," Dyche said in his post-match press conference, though he did not say which player was involved.
"One of our players made the report and I was there to be a witness to the report, not the incident."
The FA is now awaiting the referee's report from the match.
With Peacock-Farrell pressed into action due to a knee injury for Nick Pope, Burnley included three former Leeds players – Chris Wood and Charlie Taylor the others – in their starting eleven but could not compete with the quality of this current side.
"They're a side in very, very good form recently," Dyche said. "They beat Man City away, their tails are up.
"That edge you need – we've just secured Premier League football again and maybe that edge comes off, but I wasn't too disappointed."
After going a club-record nine top-flight home games without a win, Burnley will now look forward to the return of 3,500 fans for Wednesday's match against Champions League-chasing Liverpool.
"Our home fans do make a difference, as do the home fans for most teams," Dyche said.
"A lot of teams are having difficult seasons at home compared to statistical norms and we're one of them, but I'm not going to overly question my players, there's no lack of effort."