Bury Town hit six for the second time this season while Hadleigh United, Debenham LC, Framlingham Town and Halstead Town all progressed in the FA Vase.
Ben Chenery had admitted his Bury Town side were seeking revenge ahead of their Bostik League Division One North home game with Tilbury, who had knocked them out of the FA Cup at the first hurdle (2-1) at the same venue just three weeks previously.
But Bury began like a train in pursuit of victory and did it in some style as they flew into a 4-1 lead by half-time.
After the returning Leon Ottley-Gooch fired a penalty over the upright when Ollie Hughes was tripped in the box in the seventh minute, Darren Mills opened the scoring with 19 on the clock after perfectly meeting Joe White's cross on the half volley.
Ottley-Gooch atoned for his spotkick miss two minutes later, slamming home after Clarke Bogard had beat out an effort from Mills.
A downward header from Hughes from captain Bradley Barber's corner continued the goal frenzy, making it three goals for the Blues in eight minutes.
Tilbury, who had had to make two substitutions in that time, due to injuries, looked all at sea, but did get a foothold back into the game in the 41st minute when substitute Tobias Aromolaran's shot took a wicked deflection off Darcy De'ath on its way into the far right corner.
But the undoubted goal of the game followed in first-half injury time as Cemal Ramadan let fly from 25 yards with devastating effect, his shot arrowing into the top right-hand corner.
It took less than three minutes after play resumed for the second half for Bury to gain their fifth of the afternoon; Ramadan converting with a low finish from Mills' pull-back.
Bury kept up the pressure and could have had more by the time goalkeeper Bogard was shown a straight red card in the 70th minute for leaving a foot in maliciously, in the referee's opinion, on Hughes after saving twice from the striker following a goalmouth scramble.
With all their substitutes used, The Dockers had to put centre-back Joe Turpin in goal, who was greatful to see Ramadan put the resultant penalty wide of his left-hand post.
But Ramadan was celebrating his hat-trick less than two minutes later after side-footing a Hughes cut-back high into the roof of the net.
Bury will have been disappointed they did not get more, with the makeshift goalkeeper not having to show off his versatility between the posts, with Mills guilty of not squaring for a simple Ramadan finish the most guilty party.
But the first home victory at Ram Meadow this season, in four attempts, saw the Blues move up six places in the table to 7th.
Elsewhere in the division, AFC Sudbury remain a place and a point off the foot of the table having lost 3-2 at Cheshunt.
Adam Mills had continued where he left off in Tuesday's FA Cup replay win at Mildenhall by putting his side, who had only managed to pick up one point from three games, into a 14th minute lead.
But the Junior Hallett levelled two minutes later, and was to prove to be a real thorn in the visitor's side as he had Cheshunt 3-1 up at the break with strikes in the 41st and 43rd minute to complete his hat-trick.
Sudbury captain Sam Clarke, who was making his club-record breaking 377th appearance for The Yellows, gave the Suffolk side hope when he dispatched a penalty in the 72nd minute, but there was to be no late equaliser.
Mildenhall Town were left to rue a late goal robbing them of a point at home to Haringey Borough.
After Matt Green finally broke the deadlock in the 65th minute, Anthony Donald levelled things up 12 minutes from time.
But former Bury Town striker Chris Benjamin broke home hearts with his 83rd minute winner, in a game which saw Dan Brown given the home man-of-the-match award.
Needham Market remain 15th in the Bostik League Premier Division after picking up a point at Tooting & Mitcham United.
Centre-back Sam Nunn had put Richard Wilkins' side into a second minute lead, but Eddie Dines levelled on the stroke of half-time.
There were no goals in the second half as the game finished 1-1.
In the Buildbase FA Vase the quickest goal of the day was at The Millfield where summer signing Kyron Andrews had Stuart Alston's side 1-0 up inside the first minute against Wadham Lodge.
The Brettsiders doubled their advantage from the penalty spot within a minute of the second half starting, with captain Ben Elliott keeping his cool.
But there was to be a nervy finish after the Essex visitors pulled one back in the 85th minute.
There was great late drama in north London though, where Debenham LC fired their way in the second qualifying round with two injury-time strikes at Brimsdown.
After trailing 1-0 after the first half, the players were called off the pitch for five minutes due to torrential rain which threatened to see the game called off.
But the away side were mighty glad they were able to resume as Brendan Heath and then Luke Austin struck in a matter of seconds for The Hornets to land a real sting in the tail.
Halstead Town won through after extra-time in their Suffolk-Essex border derby at Long Melford.
Will Wingfield had put Melford into a half-time lead but Kane Gilbert equalised from the penalty spot in the 78th minute.
But it took until the very last minute of extra-time for Nick Wilderspin to dramatically force a winner with an overhead kick.
Framlingham Town also sealed their passage into the next round, but in much more straight forward circumstances with a 2-0 home win over Waltham Forest.
There were early exits in the competition for Haverhill Rovers, who lost 3-1 at home to Whitton United and Cornard United, who lost 2-0 at Ilford.
In the Thurlow Nunn League Premier Division Thetford Town could not be the ones to stop the Felixstowe & Walton United juggernaught as the Seasiders claimed a 5-0 victory at Mundford Road to maintain their perfect start.
Newmarket Town followed up their recent big win in the week with another fine attacking display, 5-1 victors at home to Wrxoham.
In the Thurlow Nunn League First Division, AFC Sudbury Reserves lost 5-2 at King's Lynn Reserves and Needham Market Reserves went down to a 4-1 defeat at home to Little Oakley.
Team Bury host higher-league Stowmarket Town in the FA Vase at Ram Meadow tomorrow (3pm) after the tie was switched to Bury due to Stowmarket's ongoing pitch repairs.
* For a full round-up and match reaction from the weekend's games, don't miss next week's papers.