Both sides made several changes from the 1-1 draw in the first game, with Michael Coulson, Harry Green and Will Thornton coming in for Boro, and Farsley, without injured trio Misambo, Branson and Donaldson, handed a debut to 16-year-old Acadamy player Ebenezer Ameho, writes Steve Adamson.
Boro were on top for much of the first half, without really testing visiting keeper Zan-Luc Leban, other than when a long-throw from Alex Brown was met by the head of Ryan Qualter, and the keeper flicked his effort over the bar. Frank Mulhern flashed a volley just over and Bailey Gooda thundered a long range strike narrowly wide.
Alex Purver was terrific in midfield, and he laid off to Luca Colville who fired wide, before the deadlock was broken shortly before the interval, with a trademark 30-yard free-kick from dead ball specialist Maloney, who curled the ball round the wall and inside the left-hand post, then Colville raced past two defenders before dragging his shot wide.
Farsley defended well, with centre-backs Tom Allan and skipper Chris Atkinson winning most of the high balls, but they rarely threatened the Boro goal, and a header from debutant Ameho was easy saved by Joe Cracknell.
Colville sent a terrific pass to Mulhern, who surged into the area past his marker, and his fierce low shot was pushed round the post by Slovenian keeper Leban. In Farsley’s best attack, former Boro favourite Ryan Watson had a free-kick deflected wide by Will Thornton, and from the corner by George Smith, Allan thumped his header wide.
On 71 minutes, Jordan Carroll, booked in the 11th minute, clattered into Coulson and was dismissed after receiving a second yellow card, and Boro immediately doubled their lead when Maloney sent the resulting free-kick forward to Alex Wiles, who wriggled past three defenders, and fired past Leban from the six-yard line.
It was all Boro in the last 20 minutes, Brown teeing up Dom Tear, whose shot was tipped round the post by Leban, than a Maloney cross was headed in by Tear, but an offside flag cut short his celebrations.
The third goal arrived when Maloney played a short corner to Purver, who passed back to Maloney, and the midfield dynamo cut inside and crashed another stunning 30-yard shot inside the far post.
Late on, Cracknell fisted an in-swinging corner from Ben Atkinson clear, and another Maloney free-kick forced a diving save from Leban as Boro eased into the next round.
BORO - Cracknell, Gooda, Brown, Maloney, Thornton, Qualter, Purver, Coulson (Tear 73), Mulhern (Durose 79), Green (Wiles 60), Colville
FARSLEY - Leban, Carroll, Smith, C.Atkinson, Allan, Sheridan, B.Atkinson, Leverett (Watson 60), Ameho, Silva (Morrisey 78), Stephenson (Priestly-Standing 86)
REFEREE - Lee Hible
GOALS - BORO - Lewis Maloney 43, 81, Alex Wiles 72
RED CARD - FARSLEY - Jordan Carroll 71 (2nd yellow); YELLOW CARDS - FARSLEY - Jordan Carroll, Joao Silva, Sam Leverett
BORO MAN OF MATCH - Lewis Maloney
ATTENDANCE - 958 (20 away)