Tom Prest did not display the requisite qualities as he advanced and whipped Bess straight to mid-on to the 25th ball of the day.
But Albert and Ben Brown did for over an hour. The duo showed doggedness to keep their wickets while slowly chipping away at the runs.
Albert was rewarded with his fifth Championship half-century, and first since April last year, in a gritty 138 deliveries.
It appeared Hampshire had found the blueprint to grind the match in their favour, but the pressure was always there and Yorkshire’s tight bowling and smart fields allowed Bess to make inroads.
Bess, who was captaining with Jonny Bairstow off the field with a hand injury, had positioned a leg slip for Brown. He then floated a back of a length, which turned, caught the glove of the pulling batter and landed easily in Will Luxton’s grasp.
For Albert, a deep backward point was positioned far behind square and well off the ropes. Bess’ straight delivery was swept firmly straight to the fielding trap.
Yorkshire had felt wronged by an obstructing the field appeal on the first day, they were further incensed with the umpires after Neal got away with edging to first slip on the cusp of lunch.
Bess drew an outside edge out of the batter and on first viewing, it appeared that the ball had bounced to George Hill at first slip. But a replay clearly showed that it had deflected off substitute wicketkeeper Fin Bean’s foot rather than the ground.
Their anger had subsided somewhat within 20 minutes of the interval when Jafer Chohan’s half-tracker found Felix Organ’s leading edge and looped up to mid on.
Neal had scored a maiden professional century in the One-Day Cup match on this pitch two weeks ago; he was now the main thorn in Yorkshire’s route to victory.
He batted stoically for two hours, scoring 39, but failed to keep a slog sweep down and was caught on the deep mid-wicket boundary.
There were still 43 runs needed for Nos. nine, 10 and 11 to score, but they could only combine for three of them as Kyle Abbott was lbw to give Bess his fifth wicket.
Lyth rounded off the well-fought victory by bowling Eddie Jack to give Yorkshire victory in the sort of match that demonstrates why the County Championship remains, at its best, compelling.
Report by ECB Reporters’ Network, supported by Rothesay.