Credit to the Robins for at least riding their luck and coming within five minutes of committing daylight robbery. They led 2-1 until Chertsey finally levelled with only one minute of normal time remaining.
And in extra time two tiring teams slugged it out toe-to-toe, although once more it was the visitors who had the clearer chances.
It looked like being being the classic cup tie where one team dominates but are made to pay for squandering their chances and certainly Hassocks did look more dangerous after the interval and in extra time.
But not even the staunchest home fan would argue with the result as Chertsey, lying third in their league, played some good football and looked the slicker outfit from the start.
Hassocks have lost plenty of players from last season but really the first half performance was a shambles until the last seven minutes after they drew level with an own goal.
Chertsey had gone ahead on 22 minutes when Leon Johnson's free kick from just outside the box bypassed the wall and went in off the inside of a post. The goal was greeted in almost total silence, with many of the spectators believing the ball had clipped the outside of the post.
It was no more than the visitors deserved and they could have sealed their passage before Hassocks got back on terms.
Jack Simpson pulled off a fine save from Lee O'Leary and then twice in a minute Paul Brooker lifted his shots off target when clean through. Brooker looked a useful player but his gilt-edged misses alone must have run into double figures.
The Robins levelled when skipper Stuart Faith did well to flick on Michael Eynon's inswinging corner at the near post and Chertsey No 5 Wayne Noad put through his own goal.
After that the hosts at last showed some enterprise going forward despite playing, apparently, with only Matt Russell as an advanced forward, but at the other end Simpson was relieved to see John Pomroy's first-time shot roll just wide and then instinctively stuck out his right foot to deny the same player.
After the break Hassocks continued to look more dangerous than they had but the visitors also had chances. The best home move of the match ended with Eynon's shot parried by keeper Dave Tidy before Hassocks went ahead on 70 minutes when substotute James Laing headed in another Eynon corner.
After that Chertsey chances came and went with regular abandon until their sub, Kevin Cooper, finally bundled the ball past Simpson.
In extra time it could have gone either way but no-one could begrudge Chertsey their winner three minutes from the end when Noad made amends for his own goal by pulling the ball back for No 3 Marcus Moody to supply the finish.
Hassocks: Simpson; Akehurst, Pitcher, Faith, Thompson; White, Slaughter; Percival, Hibbert, Eynon; Russell.
Middy Starman: Young keeper Jack Simpson produced the occasional kamikaze moment and indifferent kicking but he also pulled off some good saves when Chertsey were not firing high and wide.