Roberts handed the dominant Pilgrims a 23rd minute lead at The Jakemans Stadium, which Mills doubled five minutes into added time at the end of the game, as Boston stamped their authority on the first leg tie.
The hosts created a string of chances but were left counting the cost of losing centre-half Carl Piergianni to a serious facial injury with 13 minutes remaining.
Boston were unchanged once again and were straight on the front foot, determined to end their six-match winless streak against the Villagers.
An instinctive save from keeper Adam Nicklin denied Dayle Southwell from the edge of the box in only the third minute, while Nicklin later made a sprawling save to deny Piergianni.
Southwell's snapshot subsequently flew wide after Jay Rollins' cross had been blocked and looped up kindly.
It looked like being one of those nights for the home side when Nat Brown's deflected strike cannoned back off the upright with Nicklin beaten, but United finally took the lead just past the mid-point of the half with a composed, close-range finish from ROBERTS to control Southwell's pass and roll the ball into the far corner beyond the Ferriby keeper.
Piergianni's towering header was hacked off the line by Ben Middleton following Lewis Hilliard's deep corner before the same combination saw the former's header bounce to safety off the crossbar following the latter's cross. Southwell then galloped clear to fire wide across the face of goal.
Ferriby's only meaningful chance of the half saw Danny Hone stab wide at the back post on the end of Russell Fry's free-kick.
The second half was a war of attrition with Ferriby looking to the aerial threat of Tom Denton at every opportunity.
Boston went close again when Kaine Felix's piledriver nicked off Liam King and flew agonisingly wide. King then volleyed over from 12 yards as Ferriby's best chance came and went.
United's pursuit of a second goal looked like being fruitless when Rollins' dipping drive bounced back off the post with eight minutes to play.
The hosts were rewarded for their dominance deep into stoppage time when MILLS saw his own long throw returned to him by Felix and the United full-back did the rest with a sublime near post volley to stun keeper Nicklin and his Ferriby team-mates.
Boston (4-3-3): Fabian Spiess; Zak Mills, Nat Brown, Carl Piergianni (Joe Burgess 77), Dylan McEvoy; Scott Garner, Grant Roberts, Lewis Hilliard; Kaine Felix, Dayle Southwell, Jay Rollins. Subs (not used): Liam Marrs, Mark Jones, Malachi Lavelle-Moore, Cameron Johnson.
North Ferriby (4-2-3-1): Adam Nicklin; Ben Middleton, Danny Hone, Ashley Palmer, Josh Wilde; Nathan Hotte (Wayne Brooksby 51), Russell Fry; Danny Clarke, Liam King, Curtis Bateson; Tom Denton. Subs (not used): Adam Bolder, Sam Topliss, Ryan Kendall, Mark Gray.
Referee: Simon Barrow.
Attendance: 2,592 (75 visitors).