It was a case of third time lucky for the Yellamen, who had their game postponed for the last two weeks due to the weather.
Sam Wadieh headed home the opener midway through the first half before Lee Boon doubled the advantage with just over 15 minutes to go.
Substitute Jon Bennett won a penalty and then converted from the spot to give Ascot a three goal cushion.
They travel to the Isle of Wight next Saturday to take on Newport in the fifth round.
In the Hellenic Premier Division, there were excellent wins for both Binfield and Wokingham & Emmbrook.
The Moles scored four without reply at Cheltenham Saracens to run out comfortable 4-0 winners.
Callum Whitty's fine overhead kick in a dominant opening half hour set the Moles up for the victory that puts them just a point off second place.
Seb Bowerman made it 2-0 a minute into the second period and the Moles never looked back. Another goal each for Whitty and Bowerman within a minute of each other just before the hour mark put the result beyond doubt.
Wokingham & Emmbrook ended their four game losing streak with an impressive 1-0 win away to promotion-chasing Wantage Town.
A solitary first-half strike from the penalty spot, from Nick Bateman was enough to separate the two sides at Alfredian Park and move the Sumas up to eighth.
Bracknell Town were held to a 1-1 draw by Chinnor in Division One East.
Martin Bradshaw netted for his first goal since returning to the Robins but it was cancelled out by Chinnor six minutes from time.
Finchampstead were involved in a six-goal thriller at Memorial Park but had to settle for a share of the spoils in a 3-3 draw with Headington Amateurs.
Sandhurst Town's Combined Counties Premier Division match against Horley Town was called off due to the waterlogged pitch at Bottom Meadow.
In Division One, Eversley & California came from two goals down to draw 2-2 with Staines Lammas.
BRACKNELL Town have been drawn at home to Aston Clinton in the Berks & Bucks Intermediate Cup semi finals.
The game will be played on Saturday, February 23.