After Jon Rees had given the Middlesex side the lead in the fourth minute, the acting captain, Dave Hacker, cashed in with a couple before Rob Thompson, Steve Hankins and Guy Fordham added to the score.
Two Second Division clubs accounted for First Division opponents. Guildford, leading 2-0 at half-time, allowed Stourport, who beat second-placed Southgate 2-1 on Saturday in the league, to draw level but won the penalty-stroke barrage 5-3.
Beeston, newcomers to the Second Division this season, beat Slough 1-0 with a skilful individual goal from Chris Roberts three minutes from time. They prevailed despite incurring two temporary suspensions and losing their leading goalscorer, Gary Noseley, with an injury.
With Sheffield losing 3-0 at East Grinstead, Hampstead and Westminster - 3-0 winners at home to Northampton Saints - are the only non-National League side to go into today's quarter-final draw.
In the battle of the two leading Second Division clubs, Reading won 6-2 against Indian Gymkhana after Bugsy Soor had given the visitors a 2-0 lead, mainly thanks to four goals from their captain, Paddy Osborn. Cannock, who won 3-1 at Canterbury, and Teddington, 1-0 winners against Isca at Exeter, complete the quarter-final line-up.Reuse content