Rob Sheridan opened the scoring from close range in the fifth minute, and his surging run in the second half set up Jame McShane to fire past Ryan Burridge for the second.
As has been the case on many occasion already this season the Moles came up against a keeper in top form, with Burridge pulling off a string of fine saves to keep the scoreline respectable.
He even distinguished himself for the opening goal as he pulled off a terrific stop to keep out Reis Stanislaus’ header from Craig Lewington’s corner, and was unlucky to see the ball fall for the alert Sheridan to sweep home from close range.
There was a hint of controversy with the goal, as Lewington’s initial corner clipped the top of the bar before going out of play, with the ref ruling that the keeper got a touch and awarding the Moles a corner on the opposite side.
Ex Mole Lyndon Buckwell was appointed Chipstead manager on the eve of the game, and he watched his new charges from the stand as the Moles laid siege to the visitors’ goal in the opening twenty minutes, with Tom Windsor getting on the end of a fine team move but seeing his volley just clear the bar.
Burridge pulled off fine stops to deny Stanislaus and Charlie Samuels, and McShane hit an effort wide as the Moles pressed, but the game became slightly ragged as the half wore on with the Moles perhaps guilty of hitting too many long aimless balls.
Chipstead had two very presentable chances within the space of thirty seconds, but Liam Allen was equal to them on both occasions.
Molesey dominated the second half, limiting the visitors to one genuine chance that Jay Bradley put onto the roof of the net.
By that point the Moles should have been more than one in front, with man of the match Ross Chalke popping up from full back to get on the end of another fine team move that he had started deep inside his own half, but once again Burridge came to the rescue by tipping his header over.
From the resulting corner Samuels headed wide when left unmarked in the six yard box.
Burridge did well to smother at the feet of the hard working Stanislaus, before the Moles got the killer second goal with 15 minutes to go.
Sheridan made a burst from deep inside his own half before playing in McShane, who shot from the edge of the box beyond Burridge to move within four goals of his Molesey century.
The win moves the Moles up to seventh on 13 points. The last time they were in this division it took until Christmas to amass that points total and another six weeks for point number 14 to arrive, which gives an indication of how far they’ve come and how pleased they can be with the opening month of the season.
They take a well-earned rest from league action this weekend and hope to progress in the FA Cup with a trip to Croydon.