Viergever's early dismissal was further compounded when two goals from Antonio Di Natale drew the hosts level on aggregate within the opening 15 minutes.
Sociedad defender Aritz Elustondo scored his first goal for the Basque club 36 seconds into the match, but James Rodríguez headed the hosts level in the third minute and Madrid never looked back.
For all the grumblings of injustice, embittered murmurings that Jonathan Fortune should have been sent off for deliberate hand-ball before thumping the hosts level late on, there was no consolation to be found in desperate disappointment.
Goals by Liverpool old boys Peter Crouch and Charlie Adam had the hosts level at the break, but the Reds went back in front through Gerrard's penalty before pulling away for the win.
Rossi-Branco headed the hosts level from Nathan Byrne's centre.
But a powerful Keira Walsh strike drew the hosts level after the interval.
Diego Falcinelli's penalty put Sassuolo ahead but Jose Callejon headed the hosts level.
Two goals in three minutes from David Timor and Alexander Szymanowski brought the hosts level.
Derek Lyle brought the hosts level with a penalty after also winning the spot-kick.
Stevie Ward's score then brought the hosts level at 12-12 at half-time.
Suarez headed the hosts level before half-time and fired them ahead early in the second half.
