Braces from Tommy Rowe and James Coppinger plus efforts from John Marquis and Jordan Houghton helped Rovers avoid embarrassment at Stonebridge Road.
Goals from Danny Kedwell and Luke Coulson had given Ebbsfleet a two goal lead in the first half only for Rovers to score twice in added time to go in at the break level.
Ebbsfleet would finish with ten men after Chris Bush was shown two yellow cards but the result was a formality at that point.
Darren Ferguson named a strong side for the tie with Matty Blair replacing the injured Joe Wright in the only change from the previous weekend's win at Bury.
In an early indication it would not be the easiest of afternoons for Rovers, Rodney Kongolo was caught on the ankle with a lunging challenge from Dean Rance inside the first minute.
And it proved just as uncomfortable from there.
Ferguson had implored his side to take control of the ball as early as they could. But they consistently shot themselves in the foot in opposition territory, losing possession cheaply and denying themselves a hold on proceedings.
Marquis fired wide from a decent position after a fine flowing move.
But it was the hosts who looked the more threatening. Harry Toffolo was required to muscle Anthony Cook away from Myles Weston's dangerous cross.
And Coulson fired narrowly wide after an excellent counterattack.
Despite the threat from the hosts, few could have predicted how badly it would turn for Rovers and how quickly as Ebbsfleet surged clear in a two minute spell.
First, Lawlor wrestled Myles Weston to the ground after failing to claim a high ball, giving referee Lee Collins little choice but to award a penalty.
And Danny Kedwell slammed hard and low from the spot to give the National League side a 35th minute lead.
Before Rovers could catch their breath, they were two goals down.
And if they had gifted Ebbsfleet the first, they wrapped the second in a bow.
A Kedwell flick-on split Rovers down the middle and allowed Coulson all the space he could have wished for to race clear and slot under Lawlor with excellent composure.
Rovers were rattled and it took a fine fingertip save from Lawlor to keep out a high shot from Weston.
But the visitors began to settle and put pressure on the hosts' defence.
As the first 45 minutes ended, it appeared they would be heading in with one of the competition's most eye-catching half time scores.
But Rovers had a two minute blast of their own to come to remarkably finish the half level.
Rowe bundled home a bobbling ball from close range a minute into added time.
And then Marquis finished an equally scrappy effort two minutes later, slotting into an empty net after Rodney Kongolo saw a shot saved by Nathan Ashmore.
Ferguson sent on Niall Mason for Craig Alcock at the break but stuck with the same system.
The game was turned entirely on its head seven minutes into the second half as Rovers led for the first time.
In one of their most crisp passages of possession to that point, they built up play swiftly before Rowe played in Coppinger who slammed low, only for a wicked deflection to loop the ball over the helpless Ashmore.
Though it initially appeared as though Rovers would run rampant as they swarmed forward, it was soon the hosts who were enjoying greater possession in opposition territory.
But Ebbsfleet struggled to truly test Lawlor during their spell of pressure.
More to follow.