It was 2-0 after 16 minutes - and 4-0 by the hour mark as Bognor made it seven points out of nine from festive matches against Worthing, Lewes and now Whitehawk. The win lifts them to ninth in the table ahead of a home tussle with Carshalton on Saturday.
Ex-Rocks Connor Tighe and James Fraser lined up for Whitehawk as Bognor arrived at the Enclosed Ground.
In the early stages, Doug Tuck passed to Bradley Lethbridge and he ran on to it before shooting and forcing a save from Melvin Minter. Henry Muggeridge had a similar chance at the other end when he got beyond the defence before shooting wide of the post on four minutes. Smith smashed a strike over the bar when he was fed by Whyte seconds later.
Ky Marsh Brown ran across the defence before hitting an effort wide off Theo Widdrington for a corner which came to nothing. Whyte's low header after Smith's advance was easily saved soon after.
But on 12 minutes Tuck's low cross found Muitt, who hit it early and low from inside the box and into the net. Four minutes later Muitt was deemed to have been brought down by defender Lewis Broughton and the referee pointed straight to the penalty spot. He put the penalty away, sending Minter the wrong way to give Bognor a 2-0 lead.
Jason Williams was sent through as Gary Charman slipped up but with only Dan Lincoln to beat, he curled it wide. Joe Tomlinson did well to get in from the byline and he smashed a shot against the left post - and it fell to an outstretched Muitt whose shot was easily saved.
Tighe struck one over before Lethbridge committed Minter into a right-legged save. Whyte's low cross found Smith but his left-footed strike was saved before Fraser curled the ball over from outside the box. Tighe blasted over again when it looked easier to get it on target before Tomlinson shot wide at the other end.
Lethbridge was put through and his run down the left opened up the defence before he forced another save from Minter, who diverted it for a corner.
Lincoln was called into action and gave the ball away to Marsh-Brown but he managed to redeem himself with a fingertip diving save. Muitt cut inside from the right and Minter got his fingertips to push it out of the way of Smith. Seconds later Marsh-Brown's chipped cross found Williams who spun his header wide of the near post. HT 0-2
Tuck got the ball out wide to Lethbridge but after cutting inside he fired wide of the post. He got the ball in a decent position again inside the box but struck it high over the bar.Tighe was replaced by Lucas Rodriguez on 53 minutes as Whitehawk needed to shake things up.
Bognor's third goal came on 55 minutes. Lethbridge and Tomlinson combined before the ball was threaded square to Whyte, whose early shot flew into the bottom corner. And a fourth followed on 60 minutes when Smith turned his defender and hit a low shot beyond Minter.
It was a case of how many Bognor would win by now and Smith smashed one over soon after - but the Whitehawk fans continued to cheer on their team. Fraser was replaced by Nathaniel Pinney before Lethbridge was replaced by Mason Walsh a minute later.
Marsh-Brown, a threat all afternoon, shot low at goal and Lincoln saved it low to his right. Bognor sub Tommy Scutt, on for Charman, cut the ball along the deck for Muitt and he diverted the ball towards goal but Minter pushed it away.
Williams turned and shot from the edge of the box and only just wide of the right post before Walsh curled a shot at goal and Minter was equal to it again, pushing it away. Williams appeared to be offside before running through and shooting under Lincoln as Whitehawk pulled a late goal back.
But that took very little of the gloss off a fine afternoon for the Rocks - one they hope will signal a strong second half to the season.
Rocks: Lincoln, Sanders, Tomlinson, Tuck, Field, Charman (Scutt 76), Whyte, Widdrington, Smith (Wild 90), Muitt, Lethbridge (Walsh 69). Subs not used: McCormick, Osborne.