Thompson Teteh made a stunning return to the starting line-up, scoring a first-half hat-trick before being forced off with an untimely shoulder injury.
Rovers were without leading try-scorers Harry Newman and Luke Briscoe, with both players made unavailable by parent club Leeds Rhinos.
On-loan half-back Ben Reynolds, forward Daniel Smith and Ashton Golding were also not up for selection.
The hosts took a fourth-minute lead and never relinquished it, despite Swinton keeping them in check for the first 20 minutes of the tie.
Jorge Richardson and Jack Broadbent were drafted in for their competitive debuts while Jack Render filled the vacant position at full-back.
A potential clash with a Super League club awaits in the next round, with Leeds Rhinos, Hull KR, Salford Red Devils and London Broncos entering the competition in round five.
Featherstone got off to a flying start with two tries from returning Papa New Guinea centre Teteh.
The first came as he combined with Broadbent to slide over on the left.
Minutes later, he took a pass from international teammate Watson Boas and darted through a gap, stretching out to plant the ball down to make it three tries in five Featherstone appearances.
Both conversion attempts went wide, giving Rovers an eight-point advantage.
Swinton reduced the arrears to two points on 15 minutes however, as Gavin Bennion - who made one appearance for Rovers in 2014 - crashed over from close range.
Debutant Broadbent settled home nerves almost immediately as he took a superb cut-out pass from Render to dot down in the corner.
In a free-scoring first half, Broadbent was guilty of gifting Swinton a possible route back into the game.
The winger palmed a high kick backwards and top Swinton try-scorer Michael Butt pounced to ground out wide for his 50th Lions try.
Teteh was having a field day against the visitor's left-edge defence as he completed a first half hat-trick, crashing over on the left for a third time on 25 minutes.
But, the PNG centre was dealt a tough blow as he was forced off with a suspected dislocated shoulder immediately after scoring.
Rovers increased their lead to 14 points just after the half-hour mark when Scott Wheeldon burst onto a short ball from Cameron King and crashed through three players to score.
Featherstone kept Swinton at bay for the remainder of the half, and after some sustained Lions pressure, Rovers broke to increase the lead.
John Davies picked up a loose ball and offloaded to Boas who showed the Swinton defence a clean pair of heels to race over from 50 metres.
The home side were in a free-flowing mood and extended their lead six minutes into the second half.
Luke Cooper drove toward the line and from the resulting play the ball, Boas put Brad Day over on the left-hand flank.
King made himself Featherstone's top try-scorer for 2019 as he increased the lead on 55 minutes, stepping over for his sixth try in nine games.
The Australian hooker had been moved to half-back after Boas was withdrawn due to injury.
The visitors rarely threatened in the second half but did grab a consolation as Harry Aaronson finished acrobatically in the corner after Wheeldon had been sin-binned for retaliation.
Richardson was denied a debut try with seven minutes to go as James Lockwood was penalised for obstruction.
Featherstone Rovers: Render, Broadbent, Teteh, Harrison, Hardcastle, Richardson, Boas, Lockwood, King, Makatoa, Wheeldon, Davies, Day. Subs: Beckett, Cooper, Maskill, Ormondroyd.
Swinton Lions: Hansen, Butt, Forsyth, Thomas, Aaronson, Smith, Fairclough, Bennion, Waterworth, Hall, Williams, Hatton, Acton. Subs: Brickhill, Ganson, Jones, Kenga.
Referee: Liam Moore