Romford and Athletic Newham ensured their progress in the FA Vase, but Woodford Town suffered penalty pain as Barkingside and May & Baker also bowed out.
Boro had produced back-to-back Essex Senior League wins at their new home ground and completed a fine first week at East Thurrock with a 2-0 success over Crawley Green.
They took the lead after just 52 seconds when Henry Hart won a corner and Kris Newby's delivery was met by Michael Turner for a firm header into the top corner of the net.
Newby sent a free-kick just over on 10 minutes, before a long ball over the visiting defence found Charlie Morris, whose effort was handled by a defender.
Finley Purcell was sent the wrong way from the spot by Newby but pushed a shot from Flynn Hamilton wide to deny Boro a third goal.
Hassan Nalbant fired across goal after being set up by fellow substitute Lewwis Spence in the second half and Hamilton sent his shot over.
But Jake Anderson had to be at his best to keep out Keane Fullwood's header, before Green were awarded a last-minute penalty.
Lanrewajul Balogun saw his spot-kick turned away by Anderson, though, to preserve his clean sheet as Boro ensured their name would be in the hat for the third-round draw.
FULL-TIME @RomfordFC 2-0 @CrawleyGreenFC
— Romford FC (@RomfordFC) November 11, 2023
Romford’s 3 consecutive home wins are clearly attributed to a combination of a new home fortress as well as unquestionable support from our fans which has been a driving force
NOW is the time to get behind the club and show your support! pic.twitter.com/HRXddMqUrR
Athletic Newham found themselves 2-0 down after just 15 minutes at Wembley, before hotshot Richard Kone halved the deficit.
Jacques Leurs levelled on 40 minutes, with Kone putting the visitors ahead early in the second half as he took his tally for the season to 18.
Wembley squared matters once more, though, and it went to a shoot-out, with Newham winning 4-3 after two excellent saves from Lindrit Beqiri.
Can't be forgetting about the 2 saves Lindrit Beqiri made throughout the shootout #Goalkeeper pic.twitter.com/nV801PZDcC
— Athletic Newham FC (@Athleticnewham) November 11, 2023
Woodford Town came from behind to draw 1-1 at Spartan South Midlands League hosts London Lions, only to lose 5-4 on penalties.
And Barkingside saw their hopes of progress shattered by fellow Thurlow Nunn League outfit Stanway Pegasus, as Harry McDonald netted the only goal of their game on 78 minutes.
May & Baker welcomed White Ensign to Aveley's Parkside Ground on Sunday, but trailed by two goals at the interval.
Ezekiel Bademosi and Mechack Asuka put the Essex Senior League side on top, but Bakers hit back on the hour mark to give themselves hope of causing an upset.
Visiting keeper Harry Fairs denied them an equaliser, though, and Robbie Allen sealed a 3-1 win for Ensign in the sixth minute of injury time.
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