David Worrall had opened the scoring for Vale inside 10 minutes, and the Mariners had to wait until the death to get back on level terms.
James McKeown also saved a Michael Tonge penalty shortly after the hour.
New boss Jolley, who has succeeded Russell Slade, made five changes while the Valiants were missing top-scorer Tom Pope.
Once the action began, the hosts looked to get on the front foot, and they forged a first chance when Siriki Dembele struck over on the half-turn.
However, soon after at the other end, the visitors dealt a hammer blow.
A cross from the left was not dealt with by Town – and Worrall was on hand at the far post to take a touch and drill into the bottom corner.
Grimsby had chances in the second half, but they left it late as Berrett popped up in the Vale box to equalise with a cool finish.
Real Sociedad have firmed up their interest in Newcastle midfielder Mikel Merino by reportedly making an opening offer of £10.5m.
Freiburg defender Caglar Soyuncu says he has turned down offers from Turkish clubs in the hope a move to Arsenal will be finalised.
Watford will reportedly listen to offers for skipper Troy Deeney but will be looking to pick up around £10million for his signature.
Huddersfield are reportedly set to join Tottenham in the race to sign Eintracht Frankfurt's Croatia international star Ante Rebic.