Hampshire 186 for 8 (Albert 65*, Hurt 3-25, Bailey 3-37) beat Lancashire 183 (Jones 84, Turner 5-25) by two wickets
South African-born Turner's five for 25 led an impeccable fast bowling display from Hampshire, with Jack Campbell and Scott Currie removing the rest.
In form batter Rob Jones crashed 84 in a 119 partnership with Steven Croft, to take his competition average to 239, as Lancashire scored 183.
Liam Hurt's brutally quick three for 25 made sure Hampshire couldn't ease to victory but 20-year-old Albert, on the back of a match-winning 84 against Derbyshire, managed to get his side over the line with 10 balls to spare.
Hampshire's eight-wicket victory keeps them top of Group B with a perfect record, with Lancashire now three points adrift with three wins, a washout and this defeat - both will expect to make the knockout stage.
On a blistering quick wicket, having been asked to bowl by Keaton Jennings, Campbell and Turner had Lancashire seven for 3 inside five overs. Turner's first delivery of the match set the tone, with Ben Brown taking the ball at shoulder height a couple of steps in from the 30-yard circle. Jennings couldn't resist attempting to cut at one though on his return from Lions duty, but the extra bounce found his edge.
Luke Wells impatiently skied Campbell and Josh Bohannon was caught behind to a ball which gloriously shaped in.
Lancashire still hadn't scored off a run off the bat at this stage, but Jones pushed and ran to cover before unfurling a square drive to begin a very profitable, and needed fourth-wicket partnership.
Jones has been in fine form in the competition with scores of 70 and 85, both without being dismissed. Here he was effortless in reaching a 60-ball fifty, often using the bounce to his advantage.
The pair had recovered the situation before Lancashire collapsed again, with the last seven wickets falling for 57 runs. Croft was yorked by Campbell to end the county's record fourth-wicket stand against Hampshire before George Balderson clothed Turner to midwicket.
Currie then opened the floodgates with a triple wicket maiden, taking three wickets in four balls. Jones fell for the first time in this season's cup when he cut to point, Tom Bailey edged behind first ball before Will Williams defended his first ball but was pinned second. George Lavelle and Liam Hurt were both caught trying to attack Turner to give him his five.
Hampshire plodded rather than attacked the target. Ben Brown, promoted to open, was lbw to a Bailey delivery which seamed in, Tom Prest dragged a wide Hurt ball onto his stumps having been bogged down, and Nick Gubbins fell into a perfectly placed short extra cover trap off Balderson.
Hurt's searing pace had Aneurin Donald chopping down and Fletcha Middleton caught behind with a frighteningly quick delivery from his long run-up and low action. Felix Organ also hit onto his own stumps off Bailey and Scott Currie swung two boundaries before he was pinned by Luke Wells.
Sixteen-year-old debutant Dom Kelly belied his inexperience with 17 in a 38-run stand with Albert but cut to point with 18 still needed. But Albert reached back-to-back fifties in 64 balls and ticked off the remaining runs with Turner to the backdrop of a raucous crowd, with the winning runs a lofted on-drive for four.