Price’s 113 ensured that the Warriors made the most of winning the toss and electing to bat first, as they reached stumps on 290 for five.
The Warriors lost their first two Sunfoil Series matches and endured difficult limited overs campaigns, but had a productive first day under interim coach, Malibongwe Maketa, thanks to Price’s sturdy knock.
The 33-year-old put on a steady partnership of 46 for the opening wicket with David White, who was returning to action after a lengthy injury lay-off, before Ryan McLaren had White caught behind for 25.
Jon-Jon Smuts was the other batsman to fall in the morning session, and the Dolphins were granted a foothold into the match when Craig Alexander dismissed Ryan Bailey for 26 midway through the afternoon session.
However, Colin Ingram joined Price in an 83-run stand that put the Warriors well on top, and which was only ended when Imran Tahir bowled the opener with around an hour of play left in the day.
Tahir cleaned up Somila Seyibokwe two balls later to leave the Warriors 221 for five, but that brought Wayne Parnell to the crease after he had overcome a stomach bug to take his place in the Warriors side.
Parnell and Ingram carried the Warriors through to stumps with an unbroken 69-run stand, and finished the day unbeaten on 32 and 63 respectively.