The Moles put in a superb performance to beat former Vase winners Deal 5-2 away from home while Ascot saw off local rivals Reading 3-0 at the Racecourse Ground.
Binfield's reward is a home match against another Kent-based side, Tunbridge Wells, in the third round on December 8.
Ascot have been handed an away trip to Combined Counties Premier Division Colliers Wood United.
Jemel Johnson gave Binfield the lead in Kent when he headed home a Paul Shone cross in the 15th minute.
Although Deal equalised almost immediately from the penalty spot, they found themselves 3-1 down at half time after goals from James Suarez and Carl Davies.
Seb Bowerman extended the visitors' lead further and man-of-the-match Suarez rounded off the scoring after Deal pulled a goal back.
It was a different story for Ascot, who left it late to wrap up their win against Hellenic Premier Division strugglers Reading.
Justin Clayton gave Yellamen an early lead but it wasn't until the 85th minute that Ian Brooks made it 2-0 with a superb long-range effort.
Jon Bennett then added gloss to the scoreline with a third goal in added time.
Elsewhere, Sam Barratt scored a hat-trick to help Bracknell Town beat Highmoor Ibis Reserves 6-1 in the third round of the Berks & Bucks County Intermediate Cup.
Sam's brother Tom was also on the scoresheet along with Matt James and Taylor Elliott-Money.
Robins will face Reading Saturday League Premier Division side REME Arborfield in the last 16.
Sandhurst Town caused one of the shocks of the weekend in Combined Counties Premier Division as they beat high-flying Horley Town 2-1.
The win is just Sandhurst's third in the league this season and lifts them above second-from-bottom Dorking on goal difference.
In Combined Counties Division One, Eversley & California eased past CB Hounslow 6-0 to stay in contention at the top of the table.
Ricky Hogsden scored twice in the win and there were also goals for Bradley Cann, Darryl Bloxham, Sam Morgan and Neil Williams.
Wokingham & Emmbrook and Finchampstead were both without matches at the weekend.