Al Sadd triumphed in an all-Qatari AFC Champions League last-16 tie with a 3-1 victory over Al Duhail on Tuesday.
Xavi's side were the more clinical at Jassim Bin Hamad Stadium as they secured a 4-2 aggregate triumph over their Stars League rivals.
They will face Al Nassr in the quarter-finals, the Saudi Arabian side having beaten Al Wahda on Monday in the first knockout round.
Al Duhail made the early running in pursuit of a goal to swing the tie in their favour, following a 1-1 first leg draw, but Al Sadd went ahead against the run of play after 20 minutes through Akram Afif, who had a simple finish after an unselfish pass from Baghdad Bounedjah.
Bounedjah hit the post before Al Sadd got their second 11 minutes before the break, Abdelkarim Hassan blasting home a free-kick.
Edmilson got a goal back before the hour mark, but Al Sadd made certain of victory when Ahmed Yasser put into his own net in injury time, and Mohammed Muntari was sent off for violent conduct as Al Duhail frustrations boiled over.
In the later match, Al Hilal edged through 4-3 on aggregate despite a 1-0 defeat to Al Ahli in Riyadh.
The Group C winners appeared in control after a 4-2 first-leg win, but Abdulfattah Asiri's precise finish three minutes before the interval had King Saud University Stadium on edge.
Al-Hilal survived the second half unscathed, though, and will meet Al Ittihad in the last eight.