The young Reds had taken a two-goal lead during the opening 20 minutes of Saturday’s clash at the Kirkby Academy, through debutant Joseph Dixon and Charlie Huth.
But the visitors struck back to go level just before the break.
Simon Wiles’ side kept their poise, however, and delivered a dominant display in the second period that was illuminated by a Goal of the Season contender from Yeguo and a clinching blast by Farkas.
Liverpool started the U18 Premier League North fixture well and were ahead within the first few minutes, centre-back Dixon clipping home an early corner on his first competitive start at the level.
Burnley almost responded immediately and Reds goalkeeper Matty Wright did brilliantly to claim the ball at the feet of Blayz Borgesson as he tried to take it around him.
While the home side were dominating possession, there were chances at both ends, Farkas firing over for Liverpool and James Lewis curling just wide for the Clarets with 15 minutes on the clock.
Midway through the half, the Reds stretched their lead with a lovely team goal.
Zak Coxon released Yeguo down the left and his cross was met by Huth, whose first-time finish lacked power but was placed perfectly into the corner.
The two-goal advantage lasted just five minutes, though, as Burnley struck back, Borgesson pouncing from close range after Wright had turned away a free-kick from the edge of the box.
Dixon headed another corner just wide for Liverpool and Ellis Hickman brought a good save from goalkeeper Callum Feeney with a powerful snapshot after Haydn Murray-Holme’s initial set-piece was blocked.
Huth went close to his second with a tremendous shot tipped over by Feeney, but it was the away team who struck on the stroke of the break to level things up.
Wright, who had already made a great save to deny Tambwe Leonard, could do nothing a short time later when Warren Taylor swooped to make it 2-2 at half-time.
The break came at the right time for the Reds and they regrouped to dominate the second period.
It started with that stunner from Yeguo, collecting a drop-off from Farkas on the left and rifling a powerful effort beyond Feeney and into the net.
The goal inspired a period of complete control for the home side, Lenix Conde – impressive throughout – offering a driving run from full-back before dragging his shot just wide.
Conde was involved again as he released Huth down the right to send in a cross met by a stretching Coxon. The forward just missed the post with an effort that would have capped a picture-book goal.
Huth volleyed narrowly over and Farkas was denied by the goalkeeper’s legs as Liverpool turned up the pressure.
A fourth seemed inevitable and was delivered on 73 minutes, Farkas collecting a pass from Coxon, driving into the box and guiding home the finish to secure all three points.
Team
Liverpool: M. Wright, Conde, Owen, Dixon (Majekodunmi, 62), Clarke, Murray-Holme, Huth, Hickman (Eden, 72), Coxon, Farkas, Yeguo (Moran, 90).
Unused subs: Hilditch, Ekiugbo, Garan, Phillips.
Goals: Dixon (2), Huth (19), Yeguo (51), Farkas (73).
Next up
The Reds are on the road in the league next Saturday (September 19), visiting Derby County.
Kick-off is 12pm BST at the Rams’ academy.