Teenager Rory Boulding marked his full debut for the Stags by creating the opening goal for brother Michael and then adding a second himself to calm home nerves at the end of a scrappy first half.
In the 33rd minute Matt Hamshaw's incisive pass set Rory Boulding racing clear down the right wing and he crossed for Michael to tap in at the far post - his 11th goal of the season.
Six minutes later Rory made it a Boulding double, latching on to another Hamshaw pass and firing under the keeper with a fine shot on the turn from an acute angle - the first time brothers had scored in the same game for Mansfield since the Wheatleys in 1911!
Eight minutes from time substitute Ian Holmes notched his first Mansfield goal, a flicked header from yet another dangerous Hamshaw cross which looped over stranded keeper Steve Williams.
Lewes, in the first round for the third time in five years, enjoyed early possession and pressure, but failed to force home keeper Carl Muggleton into a save until the 83rd minute.
And their plight was not helped 17 minutes from time when centre-back Ian Simpemba was sent off for a second bookable offence after he tugged back Micky Boulding.
The Stags were hit by late injuries which saw centre-half Alex John-Baptiste and left winger Nathan Arnold ruled out just before kick-off. However, Jonathon D'Laryea started a game for the first time in eight months.
And they created the first chance inside the opening 60 seconds, Rory Boulding sending a dipping cross-shot, swirling in the strong wind, onto the roof of the net.
But, it was the non-leaguers who then enjoyed a spell of pressure, won the game's first corner and created a half-chance when Dale Binns burst clear down the left and Gary Holloway almost got in a shot.
In the 12th minute the Stags were unlucky when Lee Bell's 35-yard free-kick was flicked on by John Mullins and Williams had to tip the ball away for a corner.
Then Micky Boulding's tame header from Hamshaw's free-kick was easily held by the keeper.
Lewes continued to look the better side and when Bell and Mullins hesitated, another dangerous Binns cross had to be cleared off the line by the alert Dan Martin.
However, when Mansfield finally broke the deadlock in the 33rd minute, they went on to create several more half-chances in quick succession, Hamshaw and Gareth Jelleyman firing narrowly wide from 20 yards.
12-goal Paul Booth, up front on his own, finally got in Lewes' first shot in the 53rd minute, but it flew harmlessly over from 20 yards.
The Stags, looking to secure victory, were almost gifted a third goal when the keeper's sliced clearance allowed Micky Boulding a free run at goal, but he curled his shot into the side-netting.
Lewes, struggling to make an attacking impact, switched to a 3-4-3 formation in search of a goal.
But it was Mansfield who continued to make the only goalscoring chances, Micky Boulding flashing one shot across the face of goal and another into the side-netting.