
James Morris' early goal rewarded Ian Richards' men for a lively start in South Yorkshire, and Ben Jordison added a second for the hosts in the first half.
Stocksbridge - who had been on a rotten run of form since their return to the Northern Premier League's top flight this summer - proved tricky opposition, and added a third goal just after half time when Kurtis Turner rolled home his side's second via the post.
A further goal then added further gloss to the scoreline, with Luke Rawson's close-range attempt sealing a fourth of the afternoon for Stocksbridge before Ronnie McGrath bundled home a consolation for Whitby late on.
This was far from a fluent display from a Seasiders side that continued to chop and change their starting eleven, and Steels made them pay in a tetchy game at Bracken Moor to climb out of the relegation zone.
The hosts, who too had made a number of changes to their side, began brightly and perhaps should have moved in front even before their early opener. Barely nine minutes in, an in-swinging cross was met by Morris who forced a routine save from Shane Bland before Aston Ellard was denied at the back post when unmarked.
These were two glorious chances but they only had to wait a further three minutes or so to take the lead. Robson played in a free-kick and found the head of Morris who calmly nodded home an opener.
And Whitby's struggles with defending set pieces continued in the 23rd minute as Jordison was given time to bring the ball under his control and fire in a second, despite the best efforts of Connor Smith who claimed that the ball hadn't crossed the line.
Jordison headed narrowly wide as the hosts continued to push for more goals in the 35th minute, and Morris then sneaked in at the near post and miscued into the side netting when, in reality, he should have found the bottom corner of Bland's net.
Gary Liddle introduced Sam Collins, Adam Gell and Matthew Tymon at the interval, and these changes somewhat changed Town's intentions in the early exchanges of the second half, albeit without threatening Ben Townsend in the Stocksbridge goal.
But Stocksbridge got a third eight minutes into the second half. Whitby were robbed of possession and captain Turner found the net via the woodwork with a low, driven effort.
On 58 minutes, the Seasiders registered their first shot of the match. Donald Chimalilo's weaving run through the centre eventually gave Steels a reprieve as he struck narrowly off target with a drilled attempt.
Liddle responded by bringing on more attacking options in James Harrison and Jarrett Rivers and his side responded with moments of promise without really testing Townsend.
If it wasn't already, Stocksbridge wrapped up the win in the 72nd minute. It was a simple enough finish from Rawson, who collected a lay-off and fired home past Bland who did his best to make himself big.
At the other end, Townsend saved well with his feet from Harrison as the young winger looked set to perhaps open his Town account.
And there was some form of reward for Whitby as McGrath capitalised on an error from Townsend, who had spilt Tymon's initial effort, to scramble home a mere consolation goal on what was a miserable afternoon for Town.