Left-handed Billy, aged 28 and almost two years Joe’s junior, posted 43 and 110 not out in a Group Three fixture which his county dominated.
The Welshmen set Yorkshire 379 to win in a minimum of 76 overs an hour into day four, and England Test captain Joe fell for 13 as they slipped to 47-3 shortly after lunch, adding to his 16 in the first innings.
But Yorkshire’s fourth-wicket pair Adam Lyth - he posted an excellent unbeaten 115 - and Harry Brook halted the Glamorgan victory pursuit with a positive partnership of 131 until early evening, with the hosts finishing on 223 for four from 66 overs.
The players ‘shook hands’ at 5.15pm.
Joe Root was caught low down at first slip by Ireland’s Andrew Balbirnie as he played back to Dan Douthwaite’s seam.
Earlier, left-handed Billy moved from 77 overnight to 110, reaching his sixth first-class hundred - off 210 balls - with a two worked to long-leg off Joe’s off-spin.
He was greeted by applause, a fist bump and a pat on the back from his big brother.
Billy shared an unbroken 212 partnership for the fifth wicket with captain Chris Cooke, who declared immediately upon moving to 102. He had started the day on 57, with Glamorgan 161-4. They opted to begin bowling having reached 241 for four. Yorkshire then slipped to 32-2 on the stroke of lunch as Timm van der Gugten and Michael Hogan struck to bring Joe Root to the crease.
But he only lasted 18 balls, including two boundaries, as the much fancied hosts slipped to 47-3 in the 17th over.
Lyth and Brook then quickly eased the pressure, taking Yorkshire to 173-3 at tea.
Lyth - 80 at the break - pulled two sixes in a 91-ball fifty, while Brook hit one in his half-century. Heading into the evening, Yorkshire needed a highly unlikely 206 from 28 overs.
rook then punched Hogan to cover to fall for 60 in the second over of the evening – 178-4 in the 48th.
Lyth reached his 25th first-class career century off 166 balls and eased the hosts to safety.
Glamorgan claimed 14 points to Yorkshire’s 11.