A crowd of 402 saw Terry Dodd’s goalbound tenth-minute shot crashed into the roof of the net by full-back Jack Hooper and probably thought at that stage they were in line for a few more goals.
But Sittingbourne’s early-season success has been built on solid defence and when the Rocks failed to build on their lead, the game became scrappy.
The Kent side had the best of the opening stages of the second half, but also failed to turn their momentum into a goal despite one or two nervy moments at the back for the Rocks, who held on to make it through to the next round.
The Rocks made one change from the side who beat Crawley Down in midweek, Stuart Axten returning to the defence at the expense of Matt Whitehead.
James Crane switched from the centre of the back-line to left-back, while up front Luke Nightingale had not sufficiently recovered from a trapped nervve in his neck to displace either Jason Prior or Dodd.
One other piece of squad news was the departure of defender Chris Breach, who had not managed to pin down a place in the team since returning to the club in the summer - bringing to three the number of players to have left the Lane in the past week.
When the action got under way, Sittingbourne were first to threaten with Ryan Golding’s shot from 20 yards forcing Craig Stoner into a diving save.
Dan Beck and Crane almost set up Dodd on five minutes but in the tenth minute, the Rocks took the lead when Dodd was played in on goal inside the box and poked a shot past keeper Tim Roberts. It looked on its way in but Sittingbourne defender Hooper’s attempted clearance only helped it in.
Ben Johnson almost made it 2-0 on 17 minutes when his cross from the left was close to deceiving keeper Tim Roberts - who had a couple of nervy moments as the Rocks looked for a second - and creeping in under the bar. Then Johnson beat his man on the left and cut the ball back for Prior, but the striker wasn’t quick enough to react.
Stoner rescued the Rocks in the 27th minute with a brave save at the feet of Golding as he bore down on him in the box.
Johnson jinked into the box and curled a shot straight at Roberts and Beck went close with a dribble and sidefooted effort which was just beyond the post on 33 minutes.
There was a scare for the Rocks just before the break when miscommunication between Stuart Axten and Stoner saw the defender’s header loop over the keeper and almost in. The two had strong words with each other and skipper Beck had to get involved to clam things.
At the other end Beck shot wide after a great run and cut-back by James Crane.
Sittingbourne, with Joe Goldsmith on for Hooper, came out for the second half looking sharper, with the Rocks at times pinned back in their own half.
But eight minutes into the half, Johnson and Crane combined down the left to set up James Fraser at the far post for a low shot back past the keeper that was just wide.
Johnson fired wide from 15 yards after a run down the right and cross by Fraser just before the hour mark.
The visitors brought on Luke Girt for Elie Kayambe on 62 minutes and a couple of promising Rocks attacks were ended aburptly were the offside flag as the game became increasingly scrappy.
Johnson’s low shot after a mazy run was blocked by a defender and then Dodd’s turn and shot forced the keeper into a sharp save.
A third change for the visitors saw Josh West replace Golding.
Sittingbourne wanted a penalty 17 minutes from time when Girt went down in the box but the referee waved away the appeals.
Lewis Ide replaced Dodd with 16 minutes left as the Rocks adopted a more solid foundation to protect their lead.
Hicham Akhazzan found himself through with only Stoner to beat on 77 minutes but his lob didn’t have enough on it to beat the keeper who caught the shot near the edge of his box.
Sub West did beat Stoner after skipping away down the left but his cross-shot was cleared off the line by Tim Bond.
Whitehead replaced Jon Marzetti with seven minutes left, shortly before Fraser and Prior both had half-chances in a scramble in the box.
Prior had a chance to sew it up in the 90th minute but didn’t get enough power in his shot from 15 yards.
But the missed chances mattered not as the Rocks comfortably played out two minutes of injury time to progress to the next round and complete their seventh win in eight attempts this season.
Rocks: Stoner, Marzetti, Crane, Fraser, Axten, Bond, Beck, Wills, Prior, Dodd, Johnson. Subs:Whitehead, Ide, Blatchford, Wollers, Nightingale.
Sittingbourne: Roberts, Hooper, Palfrey, Coyle, Nnamani, Manners, Nuttall, Richmond,Golding, Kayembe, Akhazzan. Subs: Goldsmith, Girt, West, Nwitua, Holness, Reed.
Ref: P Lavelle (Totton)