Sumas looked to be heading out of the competition when Ian Griffin gave Highmoor the lead from the penalty spot in the 76th minute.
Matt Jones spurned a glorious chance to equalise when he missed a penalty at the other end, but he then won a another spot-kick late in the game.
This time Khalid Senussi stepped up and successfully converted to send the game to extra-time.
And Jones and Tom Williams both netted to set up a first round proper tie at home to Marlow on October 13 at Larges Lane (3pm ko).
A late fightback from Bracknell Town proved to be in vain as they lost 3-2 to Kidlington in the FA Vase.
Trailing 3-0 after 70 minutes, Bracknell hit back with a couple of quickfire goals from James Rogers and Matt James.
But despite hitting the post and going desperately close to an equaliser, Robins could not force extra-time.
Sandhurst Town eased through the second qualifying round with a 6-1 victory over Milton United.
The Fizzers will now host Wantage Town at Bottom Meadow in the next round on October 13.
John Bennett netted an 85th-minute winner to send Ascot United past Chinnor and set up a trip to Hellenic Premier Division heavyweights Witney Town in the first round proper.
Jemel Johnson and Callum Whitty scored the goals as Binfield beat rivals Reading Town 2-1 in the Hellenic Premier.
Finchampstead lost 3-0 to Woodley Town in Berks & Bucks Intermediate Cup first round.
In Combined Counties Division One, Eversley & California won 3-0 at Epsom Athletic.
* SEE THURSDAY'S NEWS FOR FULL DETAILS.