Despite going into the interval a goal down, Whitstable took only seven minutes to find a second-half equaliser.
Smith picked up the ball just outside the area in a central position and hit a shot which Hill failed to deal with.
Aaron Watson had a great chance to retake the lead for Whyteleafe moments later, running through on goal but his effort was well saved by Colmer.
Hill then managed to partly redeem his earlier mistake with 15 minutes remaining as he produced a fine save from close range to deny Whitstable substitute Robbie Rees.
Whyteleafe almost found a winner six minutes into added time, but Rodney Eruotor’s stunning effort with his left foot thundered off the crossbar.
Whitstable were denied by the woodwork in the first half of extra time, the ball crossed from the right and Sithole was at the back post waiting to tap it home, but his effort bounced off the inside of the upright and away.
But minutes later Sithole made the breakthrough, as he picked the ball up in the box, cut inside a defender, and fired his shot into the roof of the net with his right-foot.
At full time the Whitstable players celebrated in the Wembley sunshine, hugging each other in relief before sprinting over to celebrate with their jubilant supporters.
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