A Lionel Messi hat-trick helped Barcelona go eight points clear at the top of La Liga and make it a Spanish record 35 games unbeaten in all competitions with a 5-1 win at nine-man Rayo Vallecano.
Ivan Rakitic opened the scoring for Barca in the 22nd minute following an error from Rayo goalkeeper Juan Carlos before Messi made it 2-0 as he converted at the end of a well-worked move with Neymar.
Rayo defender Diego Llorente saw red three minutes before half-time for a rash challenge on Rakitic, with Messi then putting the game beyond any doubt in the 53rd minute, hitting home after Suarez had struck the post.
Manucho pulled one back for Rayo but Manuel Iturra then became the second home player to be sent off for hacking down Sergio Busquets after Neymar hit the bar with a free-kick.
Suarez missed the subsequent penalty - marking Barca's seventh failure from 12 yards in 13 attempts - but Messi completed his treble and Arda Turan added a fifth to cap off the rout.
Granada are now level on points with Rayo in the fight against relegation after seeing off fellow strugglers Sporting Gijon 2-0.
A 72nd-minute penalty from Youssef El-Arabi following Omar Mascarell's foul on David Barral and Isaac Success' injury-time strike made sure Granada leapfrogged Sporting - who had Sergio Alvarez dismissed - into third bottom.
Real Betis claimed a 3-0 away win at Espanyol to leave Barca's city rivals just two points above the drop zone.
Ruben Castro, German Pezzella and Juan Vargas were on target as Betis made it five Liga games unbeaten.
