Pre-race discussion centred on jockey Hugh Bowman's ability to get Press Statement into a good position from barrier 14 but the champion rider made the question redundant after 200m.
Bowman took advantage of a quick beginning, pressing forward on Press Statement to assume control of the $1 million event after 200m before the son of Hinchinbrook proved too classy for his opposition in the straight, striding to a 1-3/4 length success.
Press Statement gave Waller his first Caulfield Guineas success but the victory was the exciting galloper's second at Group I level after he claimed the JJ Atkins (1600m) during the Brisbane winter.
The Caulfield Guineas victory was Waller's 53rd Group I winner but the Sydney trainer was keen to deflect the accolades to Bowman.
"Great ride from Hugh Bowman,” Waller said. "The plan was to go back and get some cover but we said we don't need bad luck to win the race but he just needs to stay out of trouble, which is a bit arrogant.
"But to see him jump so well, it just makes a leading world class rider to take up that initiative to go forward after jumping so well.”
Waller did not rule out giving Press Statement a shot at the Cox Plate but would give the valuable performer time to recover from his Caulfield Guineas win before deciding whether to run him in Australasia's weight-for-age championship in a fortnight.
"We've got to see if he can beat a few others in the stable first,” Waller said.
"It would be a pretty big ask to go that far. Does he need to? Is it going to change his value? I don't think so.”
The Pat Hyland-trained Lizard Island finished well from midfield to grab second ahead of Ready For Victory, who raced behind the speed and stuck on well.
Victoria Derby hopefuls Sovereign Nation and Tarzino turned in solid trials for the Flemington feature when finishing fourth and seventh respectively, the latter after having little luck in the latter stages.