Tullius made a winning first appearance for trainer Andrew Balding when gamely landing the Makfi Suffolk Stakes at Newmarket.
Formerly trained by Peter Winkworth, the four-year-old was held up in rear in the early stages by Jimmy Fortune before coming through the field to make his bid.
The 12-1 shot stuck on well on meeting the rising ground to hold Memory Cloth by three-quarters of a length with Fury five lengths away third.
Balding said: "He's done that very well. All he did was improve for Peter Winkworth last year.
"He looks to be a useful prospect, who has grown up both physically and mentally.
"I suppose he could be a Hunt Cup horse. I will have to talk to Nick Robinson, who runs the Kennet Valley Thoroughbreds (owners) about that.
"I imagine he would go straight there if we decide to go for it."
Fortune said: "They went a nice gallop and he travelled well. He's fit and likes the ground.
"He's only a small horse and doesn't take much getting ready."Red Quartet (12-1) just held the late challenge of the 5-1 favourite Mince to land the Al Rayan Handicap.
Robert Eddery's colt wandered around up the rising ground after hitting the front but still hung on by a head in the hands of Andrea Atzeni.
Democretes was two lengths away third with Personal Touch fourth.
Eddery said: "This horse ran well at Newbury though the gound was sticky and it didn't really suit him.
"I've increased my string this season with nine more horses and I have eight two-year-olds, some of which will be out soon."
Rewarded, the 100-30 favourite, got up in the last stride to snatch the Qipco Supports Racing from Archbishop for trainer James Toller and jockey Kirsty Milczarek. However, Milczarek was banned for seven days (May 19-25) for using her whip above the permitted level.