
The Hornets took the lead when Joao Gomes, in for the unavailable Gary Martin, netted a 26th-minute opener.
But former Darlington winger Jarrett Rivers levelled shortly after half-time before Liam Murray turned the game back in Hebburn's favour with 15 minutes of normal time to play to send the visitors into the First Round Proper.
Whitby had put in an uninspiring first-half performance, however the second-half was improved yet still not enough to book the Seasiders' place in the next round of the FA Trophy.
Shane Bland was looking for a second straight clean sheet following Tuesday night's 0-0 draw with Prescot Cables and had a couple of early warning signs from the Hornets - the first in the seventh minute, when Oliver Martin's low strike fizzed just wide of the far post.
He then saw Martin strike the post, again with a low strike.
It was, therefore, in keeping with the run of play that Hebburn took the lead; a ball through the centre forced Bland out of his goal and Gomes got the first touch before tapping beyond the Whitby gloveman.
In the 33rd minute, Gomes headed over the crossbar after Jack Foalle had picked him out before Whitby finally registered their first shot of the match when Layton Watts went for an audacious attempt from distance after spotting Daniel Cameron off his line, but his effort was just too high.
At the beginning of the second half, Whitby improved following what must have been a strong half-time team talk. For the first time in the match, the hosts began to find themselves on top of proceedings, and Hebburn netminder Cameron could do nothing to keep out Rivers' well-placed low strike in the 51st minute.
Cameron made a brilliant save before the hour mark as he made himself big to parry a Jake Charles effort, then shortly after his opposite number Bland was equal to a shot from Joseph Posthill.
But Murray proved to be the matchwinner was he forced home in the 75th minute with a bulleted right-footed shot across Bland, into the far corner of his net.