The visitors made a determined start and took an early 6-0 lead with a converted try by centre Nick Nanyn.
The Dons drew level with a length-of-the-field converted try by winger Nev Morrison, who showed good speed to hold off the cover after intercepting a pass.
Prop Mark Castle sent full-back Tom Hodson over from close range before hooker Kyle Kesik weaved his way over from close range. Record try-scorer Lee Waterman, whose kick-through helped create the position, crossed for Doncaster’s fourth try just before the break.
Swinton had a man sent-off and another sin-binned, following a flare-up two minutes into the second half.
Doncaster, who had Waterman sin-binned, added to their lead when hard-working Craig Robinson set-up the chance for young half-back Richard Wilkinson to cross in style to make it 30-6.
Swinton rallied, second-rower Danny Bridge powering his way over for a converted try.
But their joy was short-lived as Wilkinson hacked on a loose ball 40 metres out and won the race to score. Sanderson again added the extras.
But far from 12-man Lions wilting in the heat, they roared back in style with Andy Ackers, James Brown and Ed Barber all crossing to leave the Dons, traditionally strong finishers, hanging on in the final minutes.
Doncaster: Hodson, Sanderson, Welham, Waterman, Morrison. Cooke, Miller, Carbutt, Kesik, Wilson, Snitch, Starling, Emmett. Substitutes: Castle, Robinson, Wilkinson, Dunn.
Swinton Lions: R Hawkyard, Burke, Barber, Nanyn, Peet, Ainscough, Atkin, Morrison, Ackers,Menzies. Bridge, D Hawkyard,Brown. Substitutes: Barlow, Johnson, Bennion, Hulme.
Referee: J Bloem.