Danny Earl, Flynn McNaughton and Will Annan also netted for the home side, but Earl was sent off for two yellows much to the frustration of manager Agnew.
The Seasiders chief said: “This was the ideal way to end 2021 with three wins during a tough run of games as we look to get away from the relegation zone.
“I asked the lads after the Marske 5-0 loss that we take the good parts out of that display - we let in three late sloppy goals - and put them into the important run of games we had coming up.
“I cannot fault the lads at all as they have done exactly that and we have gone from being at the bottom at the start of December to being within striking distance of some of the mid-table side now
“We started a bit sloppily against Pickering on Monday and they went ahead after I failed to clear a ball, and we missed another couple of chances to clear it before Lewis Taylor scored with a great finish.
“I said to the lads before the match not to let the fact that we knew some of the Pickering lads from them playing for us before to affect how we approached the games, the main objective was to get the three points.
“Lewis scoring that goal and putting them in front reminded them we did not want one of our old players to beat us, so it acted as a kick up the backside to us.
“I found a bit of pace from somewhere to break free and finish well to level the scores, then I earned a free-kick which Danny Earl put away for us to be 2-1 ahead at the break.
“We didn’t deserve to be in front at the stage as Pickering had been the better side, but we had a good chat at half-time and we came out of the traps brilliantly after the interval and scored three quick goals.
“We were superb for the first 20 minutes of the second half and we put the game to bed.”
Agnew was less impressed with Earl’s second caution which saw him receive his second red card of the season.
He said: “Danny then got stupidly sent off and this will mean he now misses a game or two through suspension.
“We need to be smarter there, at 5-1 up with only a bit of the game to go we should see it out.
“This sending-off gave them a bit of a lift and upset our team’s structure so they put us under some pressure and got a second goal.”
The player-manager has not got his sights set firmly on starting 2022 with a bang in their game at fifth-placed Cleethorpes Town.
He added: “It will be another tough game for us at Cleethorpes on Saturday as we start a very tough January list of games.”
Loan signing Luis Adlard made his debut against the Pikes, after joining the Seasiders last week on loan from Grimsby Town, while midfielder Declan Parker has signed dual registration forms with NCEL Premier Division side Handsworth.
Agnew said: “Luis has come on as sub against the Pikes when we were down to 10 men so it was difficulty for him but he showed some good touches and it is good to get him in.
“We now have a good thing going with Grimsby having also got Jaz Goundry in and he’s done superbly since he came in. We would love to see Jaz’s loan deal extended again, he’s having a great time here and is a great lad.
“Declan Parker has signed dual forms with Handsworth as he is keen to get some games in, with Peter Davidson and Nathan Hotte doing well in midfield it’s been hard for him to get into the team recently.”
Pickering started the better with Omar Sanyang having a long-range effort tipped onto the bar and over by James Hitchcock.
It took the visitors just 12 minutes to go in front when the home defence hesitated after Wayne Brooksby went tumbling in the penalty area and, as play was allowed to continue, Lewis Taylor steered the ball past his former Bridlington teammate Hitchcock.
On 17 minutes Pickering’s Dominic Joynes became the first of eight players shown a yellow card during the game when he brought down Danny Earl and six minutes later the Bridlington man followed him into referee Benjamin Duffill’s notebook after challenging for the ball with James Armstrong.
However, Pickering goalkeeper Leigh Overton escaped a booking when he appeared to handle the ball way out of his area.
After half-a-hour Agnew received the ball from a throw-in then turned to cut inside and make his way along the edge of the penalty area before firing past Overton to level things up. Sanyang again struck the bar, but the Seasiders were well in the game after a stuttering start and Agnew sent a header narrowly wide
Two minutes before half-time Harry Lovick became the latest player to be shown a yellow card by fouling Agnew on the edge of the area. His team were punished further with Overton only able to parry the free kick from Will Annan and Earl followed up to hit the ball into the net to give the hosts a 2-1 interval lead.
Before the resumption the Pikes swapped James Armstrong for Will Taylor, but within the first 15 minutes the game was as good as won when the Seasiders scored three times.
Two minutes into the half Brid skipper Pete Davidson was brought down in the area by Jack Johnson and Agnew stepped up to rifle the spot-kick past Overton.
Two minutes later an attempt by McNaughton took a deflection on its way into the goal.
After a further two minutes Lewis Taylor was injured and was carried off the field to be replaced by Brandon Holdsworth.
McNaughton struck a post following a move involving Nathan Hotte and Annan then just before the hour Earl made his way into the area before squaring the ball for Annan to strike home.
Both sides made substitutions before Earl was dismissed in the 74th minute for a second bookable offence and within a minute substitute Luke Jones had pulled a goal back for the Pikes to complete the scoring.
There were two late bookings for Brooksby and Sanyang as Bridlington went on to their biggest league win of the season.
This Saturday the Seasiders travel to the Myenergi Stadium in Grimsby to take on Cleethorpes Town.
The Owls are in fifth position but have an indifferent home record having won just three and lost four of the nine games played.
The corresponding match on August Bank Holiday went the way of Cleethorpes with a 2-1 victory. Second half goals from a Harry Middleton penalty and Jack McMenemy gave the Owls a two-goal lead before goalkeeper Tom Jackson put through his own goal in the last minute to give his former side a consolation.
Bridlington Town: Hitchcock, Dixon (Lewis 62), Barkworth, Davidson (c), Goundry, Bulless, Annan (Dennison 80), Hotte, Agnew, Earl, McNaughton (Adlard 67)
Pickering Town: Overton, Johnson, Joynes (Jones 68), Armstrong (W. Taylor 45), Clappison, Lovick, L. Taylor (Holdsworth 52), Barker, Logan, Brooksby (c), Sanyang
Unused substitutes: Thornton, Barnes
Referee: Ben Duffill