Six-time champion Ernie Els kept his bid for a seventh title alive by ousting Andres Romero 6 and 5, while Henrik Stenson and Hunter Mahan also advanced to the semifinals.
Stenson, winner of the Accenture Match Play Championship in California in February, had an impressive 7 and 6 victory over Anders Hansen, who beat British Open champion Padraig Harrington on Thursday. Hansen had a hole-in-one at the 10th.
Mahan, the last of three Americans left in the tournament, trounced Soren Hansen 6 and 4.
In Saturday's semifinals, Cabrera plays Mahan and Stenson meets Els.
Cabrera took a three-hole lead after hitting two birdies and an eagle on the first five holes. His eagle at the long fourth came after a 5-wood second shot rolled within one foot of the flag.
Casey won the sixth and seventh, but Cabrera kept a one-hole lead at lunch. He won the first hole of the afternoon with a 20-foot birdie and was four up with nine to play.
He then chipped in a crucial shot from the rough to save par on the 10th and halve the hole.
'That was a big turnaround,' Cabrera said. 'I thought I'd lost the hole but I got a half. It felt like a win.'
Els won the first two holes against Romero with birdies, then bogeyed the next two and lost both. He pulled away with four birdies in the last seven holes on the back nine to go into lunch four up. Els was seven holes ahead with seven to play, but Romero won the next two before Els finished the match by holing a 35-foot putt at the next.
'I was a little out of synch with my irons this morning but my short game saved me,' Els said. 'I'm really striking the ball nicely and I made some good long putts.'
Stenson was even better, using superb iron play to get birdies at five of the last seven holes in the morning against Hansen. He led by four then and by eight after 27 holes.
Stenson has struggled with his game in recent weeks, after becoming a father three months ago.
'Maybe the head hasn't been in the right place,' he said. 'I think this was the right event to get me going.'
Mahan, who upset Justin Rose on Thursday, took the lead at the fourth against Soren Hansen and gradually pulled away.
'I played very well and solid this afternoon and didn't make it easy for him,' Mahan said. 'Angel is playing really well but I'm looking forward to taking him on.'
Earlier, Stenson and Romero completed first-round victories in matches delayed by fog Thursday morning.
Stenson eliminated Woody Austin 1 up, while Romero beat Niclas Fasth 3 and 2.