It was a second win in just four days for Rebels and one that saw them close the gap on leaders Folkestone Invicta to four points.
Worthing put in a dazzling display with a 5-1 win over Whyteleafe on Saturday but Tuesday was a more workmanlike showing.
However, Rebels got the job done thanks to strikes from Harvey Sparks and joint boss Gary Elphick.
Despite closing the gap on leaders Folkestone, joint manager Jon Meeney wants his side to remain focused and said: “It’s nice to move up into second position but we won’t be getting too carried away.
“We have not achieved anything as of yet and it’s important we remain grounded.
“After losing last Tuesday at home to Dorking Wanderers, our response has been great.
“To win 5-1 on Saturday and also get the three points in this one is great for us.
“Back-to-back wins are always nice in this league and it’s nice that we have managed to get these victories.
“Chipstead were well organised and tried to frustrate us. They allowed us a lot of the ball and sat back a little.
“But credit must be given to us, we made the breakthrough and just kept going after that point and were well deserving of all three points at the end of the game.”
Elphick almost gave the home side the lead after just 13 minutes on Tuesday. He headed Brannon O’Neill’s corner back towards goal only to see his effort cleared off the line by Francis Quarm.
Rebels continued to push forward and went close again four minutes later. Sparks’ deep cross found Will Hendon, who took the ball in his strike before seeing his fierce shot saved by Milan Stojsaveljvic in the Chipstead goal.
Omar Bugiel was provided with Worthing’s best chance on 22 minutes. Some fine football saw O’Neill set Jordan Clark free down the right and he cut the ball back for an unmarked Bugiel, who saw his shot deflect off a visiting defender and go wide.
Worthing did finally take the lead five minutes before the break. Bugiel was once again involved as he crossed for O’Neill, whose effort was blocked, before Sparks was on hand to fire home the rebound.
Chipstead should have levelled on 56 minutes. Adam Moriarty chipped a free kick into Charlie Carter’s path but the forward could only fire wide from ten yards.
Rebels’ first real chance of the second period fell to Callum Overton. Goalscorer Sparks broke down the left before finding Overton but once again Stojsaveljvic was equal to his attempt.
Worthing did finally bag a second 23 minutes from time. Elphick was left unmarked from O’Neill’s corner and headed home to all but secure the three points.
A third almost came late on when Chipstead’s Michael Olarewaju miscued a Clark cross but the ball went just wide.
After four successive home games, Rebels are now on the road for three consecutive league games. They travel to Tooting & Mitcham on Saturday, are away to Sittingbourne on Tuesday and then head to Ramsgate on December 5.
WORTHING: Banks; Clark, Elphick, Heath; Axell, O’Neill; Hendon, Overton, Richefond, Sparks; Bugiel. Subs: Pope (Overton), Quirke (Axell), Edwards (O’Neill), Newton, Fagan.
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