
Despite creating the majority of the goalscoring opportunities in the opening stages, the Seasiders fell behind through Callum Gribbin's low finish before Jacob Hazel equalised before the half-time break.
However, Luca Navarro's second-half penalty put the hosts back in front before they doubled their lead, courtesy of Navarro's stunner.
Olly Thornley sent the Boro into a three goal lead, and despite a late fightback from Whitby which saw Hazel and Harry Green find the net, the Blues returned home empty handed and moved down to eighth in the Pitching In Northern Premier League Premier Division table in the process.
Lee Bullock and Nathan Haslam made five changes to the side which drew 0-0 against Basford United the previous week as Jameel Ible was handed a start at right-back, whilst Jonathan Burn, Malik Dijksteel, Hazel and Green returned to the side.
Ible's return at right-back saw Soni Fergus moved into midfield where Priestley Griffiths dropped to the bench.
Hazel, who remains the division's top scorer, went close to netting his 22nd of the season after curling just over the bar following Josh MacDonald's troublesome corner delivery.
Whitby were unfortunate not to take the lead in the 26th minute as MacDonald's ball found Dijksteel one-on-one with Jack McIntyre who saved well with his feet.
After Radcliffe struggled to clear their lines after this opportunity, they took the lead completely against the run of play in the 31st minute as Gribbin rolled the ball into the bottom corner of Shane Bland's goal from just inside the area.
Whitby pushed for an equaliser and got it almost instantly through Hazel as he latched onto a ball over the top, flicked it over the head of Jo Cummings before drilling home along the ground for his 22nd strike of the season.
In the 39th minute, Whitby went close through Dijksteel's strike from range which drifted just wide of the post, before there were shouts that the ball had crossed the line right on the stroke of half-time but without a conclusive view, the match officials were not able to give the goal to Town.
A strong start after the restart resulted in a breakthrough for Radcliffe as Navarro netted his first goal of the afternoon. As he raced onto through ball, he was adjudged to have been caught by Burn inside the area and the Radcliffe man stepped up to score from 12-yards.
In the 53rd minute, Radcliffe doubled their lead through Navarro as the exciting attacking player looped the ball over Bland from the edge of the area and into the roof of the net.
In the 63rd minute, Radcliffe extended their advantage as Thornley got his first of the season. After a Matthew Crothers free-kick found him, the centre-back back-heeled the ball into the net beyond Seasiders goalkeeper Bland.
Whitby had to weather an attacking storm before Hazel pulled a goal back with a stunning free-kick from just outside the area in the 89th minute to get his 24th of the campaign.
Despite a difficult second half, Whitby surged forward in the dying stages and added a third through Green who lashed a strike into the roof of the net from a tight angle.
Any momentum that Whitby were building in stoppage time, which had been extended after an injury to goalkeeper McIntyre, was soon lost as Ible was sent off following an off-the-ball incident.