It was the highest partnership for any wicket in the county's 151-year history, and only the 13th time in first-class cricket that any stand passed 500 runs.
Glamorgan finally parted the pair when Prince was out for a career-best 261.
Petersen, having batted for more than eight hours, then fell six overs later for 286 -- also the best of his career -- with Lancashire 625 for four on the second day of the match at the Welsh seaside resort of Colwyn Bay.
They declared on 698 for five, their fifth highest-ever score.
(Reporting by Steve Tongue, editing by Mitch Phillips)
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