Further strikes from Yordan Yordanov and Trystan Mayhew helped to see off the Hertfordshire outfit and set up a home tie in the last eight.
Battle took the lead after just two minutes; Yordanov slicing a half-volley from the edge of the box into the corner of the net.
The Baptists were in ecstasy only two minutes later when Boyd stood up a high cross to the far post and Mayhew outjumped the goalkeeper and full-back to head home.
Battle were now playing some great football, moving the ball quickly and intelligently, and winning possession back with urgency and exploiting weaknesses wisely.
They were excellent value for their lead and the back four of Ian Rafati, Ollie Jeffs, Tom Saunders and Mark Dowling were largely untroubled, with much of the game being played in Roman territory.
A whipped free kick from Saunders was headed narrowly wide by Adam Higgins-Gooch. The Hertfordshire hosts struggled to hang on to the ball as the tenacious central midfield duo of Dale Vinall and Glenn Carrick worked efficiently to disrupt the home team's impact.
Then on 25 minutes, Boyd extended the lead further when he struck a 25-yard free kick into the net off the junction of post and crossbar.
Even a first half injury to Yordanov couldn't knock the East Sussex representatives off track as his replacement Finlay Garlick demonstrated positive forward play and the Baptists closed off the half looking unassailable.
The early part of the second period saw Romans rally, putting Battle under some sustained pressure as they kicked with the breeze.
With a comfortable lead the Baptists became complacent, wasting possession and inviting pressure, but despite their improvement, Romans still couldn't break down the Battle defence, and goalkeeper Jake Rudwick didn't need to make a save of note.
Battle stepped things up again in the final third of the match. Boyd whipped a cross to the far post and the ball sailed over the goalkeeper and under the crossbar to make it four.
A few minutes later, left-back Dowling fed man of the match Boyd, who danced through a legion of players and fired left-footed high into the net from 20 yards to complete his hat-trick.
With the game ebbing away to the inevitable result, the Baptists gave a first team debut to young Ben McNeill, who almost forced a late chance in the closing moments.
Battle will face Milton Keynes-based Clean Slate, who recorded a 2-1 win against Christians in Sport (Luton), in a quarter-final scheduled for February 25 at Battle Recreation Ground.
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