Klich capitalised on a defensive error to double Leeds' advantage on the stroke of half-time, and second-half efforts from Helder Costa and Klich again gave the hosts their fifth straight win.
Said Benrahma made it 6-0 from the penalty spot in the 71st minute before Dasilva was given the chance to complete his hat-trick also from the spot.
Bristol City also made a significant statement as they beat Huddersfield 5-2 to move up to fifth place.
Nathaniel Mendez-Laing's effort from outside the box in the 14th minute was enough to give the visitors their first away win of the season.
Wayne Rooney took his place in the Derby dugout for the first time but the Rams' new player-coach could not inspire his side to victory over Queen's Park Rangers.
Bottom club Barnsley claimed their first win since the opening day of the season with a 3-1 success over Hull at Oakwell.
Goals from Alex Mowatt and Mike-Steven Bahre put Barnsley in command and despite Keane Lewis-Potter giving the Tigers hope with an 81st minute header, Conor Chaplin's injury-time effort confirmed the three points.
The home side looked in control after Joe Garner's 34th minute opener but Puscas levelled from the penalty spot on 79 minutes, scored his second a minute later, and completed his one-man show in the 84th minute.
Bradley Dack scored at both ends as Blackburn piled more pressure on struggling stroke with a 2-1 win in the Potteries.
Dack scored his 10th goal of the season in the 13th minute but cancelled himself out when he scored an own goal 10 minutes from time.
Fortunately for Dack, team-mate Sean Gallagher was on hand to slot home four minutes later and preserve the points for Rovers.
Steven Fletcher scored twice as Sheffield Wednesday eased to a 3-1 win over Charlton at The Valley.