Efforts from Keinion Robinson, Cameron Peters and Robbie Burns were enough to help Hook bag a 3-1 extra-preliminary round replay win at Culver Road.
Just as in the original tie three days earlier, Lancers went 2-0 behind.
Alex Bygraves pulled a goal back just before the break but Lancing could not find a way back in.
Lancers assistant manager Nigel Geary was left frustrated at the Cup exit.
He said: “It just wasn’t our night. We made the players aware that the first 45 minutes were not good enough and we improved in the second half.
“James Wotherspoon had two shots cleared off the line and he hit a post. We had so many chances but if you don’t take them you will be punished.”
Robinson fired Chessington ahead after 20 minutes, then Peters added a second 15 minutes later.
Bygraves’ header back across goal found the bottom corner a minutes before half-time to get his team back in it.
Wotherspoon had an effort cleared off the line on the hour before striking a post ten minutes later.
Chessington ensured it was they who progressed after 75 minutes with Burns adding a third for his side.
Lancers had fought back from two goals down on Saturday to earn the replay.
First-half efforts from Basary Morally and Kienion Robinson had left Lancing with it all to do as they went into the interval 2-0 down.
Lancers were inspired in the second 45 minutes, though, managing to get back on level terms by the hour mark.
Lucas Tredrea pulled one back for John Sharman’s side eight minutes after the restart, then Lewis Finney made it 2-2 after an hour.
Both teams had chances to go on and win the game but it finished all square.
Lancers manager Sharman was relieved his team were given a second bite of the cherry with a replay and said: “It would have been a shame to have gone out on a poor performance.
“We were pleased to claw ourselves back into the match and gain a replay. They had players that caused us problems and we were fortunate not to be 3-0 down at the break.
“Numerous players were unavailable for various reasons so we changed from our usual formation, which may have been a reason behind our slow start.
“We managed to adapt, grow into the game and get back into it, having chances to win it.”
LANCING v Chessington & Hook United on Saturday: D’Cruz; Pittock, Emery, Bygraves, Sharman, Bunch, Williamson, Wotherspoon, Fair, Tredrea, Finney. Subs: Donaldson (Wotherspoon), Blogg (Bunch), Sibanda, Baker, Arnoux.
LANCING v Chessington & Hook United on Tuesday: D’Cruz; Marsh, Sharman, Bygraves, Pittock; Williamson, E.Finney, Wotherspoon, Tredrea, L.Finney; Fair. Subs: Emery (Piittock), Bunch (Wotherspoon), Donaldson (Tredrea), Blogg.
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