
The Seasiders, targeting a league double over their opponents following an opening day win in August, were unable to muster a number of clear-cut goalscoring opportunities at the Towbar Express Stadium, with Ben Farrar going to the closest for the hosts in the first-half.
Gary Liddle's men, though, were resolute in defence when required and restricted the visitors as they recorded a rare clean sheet.
Three changes were made from Boxing Day's league defeat against Morpeth Town, with Farrar handed his full debut since arriving on dual-registration from National League side York City last week, while Adam Gell and Michael Woods were both awarded starts.
Shane Bland was forced into early action as the 31-year-old goalkeeper blocked Steven Rigg's fierce strike from the edge of the penalty area, getting an important hand to the ball.
Farrar, who was in fine goalscoring form on loan at Bridlington Town earlier this season, went close to opening his Whitby account for the current campaign after his drilled effort from a tight angle, following neat link-up play with Woods, was struck into the side netting.
Farrar was unable to fire the hosts into the lead before half-time as the young striker directed a diving header into the hands of Alex Mitchell.
In the second-half, James Harrison, introduced from the bench, was unable to make a goalscoring impact as the pacey winger, with just one Whitby Town goal to his name to date, completed a darting run into the box before Workington goalkeeper Mitchell produced a save at his near post to prevent the Seasiders' man from firing home.
Shortly after, Mitchell stood firm to keep out a long-range Lewis Hawkins attempt, gathering his fierce strike with relative ease.