The Blues were without talismanic striker Danny Brunskill through injury and dropped defender Lee Pallender who made a series of mistakes during Saturday's defeat at Matlock.
In came player-manager Phil Brumwell for his first start of the new campaign and there was a recall for local forward Tom Raw.
But visitors Kendal made all the early running and grabbed a shock lead inside three minutes. A simple long ball led to a breakdown in communication between skipper Richard Forster and goalkeeper Ben Escritt.
The towering figure of Craig Hobson barged past Forster and round the onrushing Escritt on the edge of the box, before side-footing into an empty net.
Two minutes later and, unbelievably it was 2-0 in almost identical fashion. Another long punt down the middle of Whitby's defence saw Hobson breeze past Forster and slot past a helpless Escritt.
Alex Taylor then fired wide from the edge of the area as Kendal threatened to run riot before the shell-shocked home side got out of the blocks.
Whitby's first chance came on 11 minutes when Karl Charlton's lively effort was a whisker away from finding a top corner of the Kendal net.
The resulting corner was hooked over his own head and back into the box by Charlton, with Tom Raw beating keeper David Newnes in the air, only for Tony Hackworth's goalbound drive to be cleared off the line.
The loose ball found its way to Andy Burton, whose right-wing cross was drilled goalwards but blocked by a Kendal defender for a second time, amid loud shouts for handball.
On 20 minutes, Hackworth and Raw again combined, but found the visitors' big back line again able to block close-range efforts.
At the other end, the lively Lee Mulvaney waltzed his way unchallenged to the edge of the Whitby area, but ended up hammering wide of the target, with a diving Escritt having his nearest post covered.
Six minutes later, Taylor dispossessed Forster and fired first time inches wide from 20 yards.
But despite these scares, Whitby struck back on the half hour.
Raw was rewarded for his perseverance as he reacted quickest to Hackworth's deflected header down to drive clinically past Newnes from just inside the area.
As Whitby finally started to get the ball on the deck, another scramble in the Kendal area again culminated in Kendal's big defence making a last-ditch block, this time from Charlton.
Burton then beat full-back Paul Byrne down the right flank and drove an awkward ball towards Hackworth, who could only pick out Newnes from a good position.
Burton again did well minutes later, holding the ball up well and winning a free-kick by the right corner flag. Charlton's inswinging far post cross was headed wide by Forster. And the central defender's bad afternoon was rubber stamped in first-half injury time when another innocuous through ball found Hobson who eased past him for a third time and drove past Escritt for probably the easiest hat-trick ever scored at the Turnbull Ground.
It was a real hammer blow for the Blues on half-time, Forster and the unlucky Charlton made way for veteran Lee Nogan and teenage winger Sam Garvie.
The visitors wasted a good opportunity early in the second half, when Hobson again created chaos and forced Ashley Lyth to drag him back by his shirt on the edge of the Whitby area, but the resulting Michael Cole free-kick was curled well wide.
Moments later, full-back Neil Murphy did better with a surprise swerving effort of his own from distance which flew inches from Escritt's right-hand post.
Whitby were looking brighter and tried to bring the wings into play at every opportunity. On 54 minutes, a left wing cross was hooked narrowly wide on the turn by Alex Janes.
The Blues then powered back into the contest on the hour mark, with both subs heavily involved. Garvie tricked his way to the byline and drove across goal, with Janes turning the ball back into the box at the far post and Nogan keeping his composure well under pressure 12 yards out, to take a touch and fire low past Newnes for 2-1.
With 20 minutes left, Nogan went down with a head injury inside the Kendal box, but play continued with Whitby in possession and Janes' pinpoint left-wing cross was nodded into the side netting by stand-in captain Hackworth.
During three minutes of injury time, the Blues were granted one last chance to grab a share of the spoils.
But again both new men, Nogan and Garvie saw shots blocked by the heroically robust Kendal backline.
Whitby: Escritt, Brumwell, Janes, Lyth, Forster (Nogan 45), Tinkler, Huggins (Thompson 81), Burton, Raw, Hackworth, Charlton (Garvie 45).
Whitby Co-operative WTFC man of the match: Mark Tinkler – adjusted well to playing in defence for the second half.
Match sponsor: The Kaye Family of Ripponden. Match ball sponsor: Bothams of Whitby.
Attendance: 302

Result: Whitby Town 2 Kendal Town 3