Surrey 136 for 3 (Finch 67*, Maddinson 41) beat Hampshire 133 for 7 (Northeast 37) by seven wickets
Surrey can still qualify for the quarter-finals of the Vitality Blast after inflicting a ninth defeat in 13 games on Hampshire at the Kia Oval.
They cruised to a seven-wicket win with 15 balls to spare after restricting Hampshire to 133 for 7 with Aaron Finch leading them home with an unbeaten 67.
Victory moved Surrey above Sussex into fifth but they will need to beat Glamorgan in Cardiff on Friday to have any chance of a top-four finish, and even that will depend the results of their rivals in the final rounds of south group games on Thursday and Friday.
Hampshire hopes had been briefly raised when Afghanistan off-spinner Mujeeb Ur Rahman bowled Jason Roy round his legs for a duck in the first over. Dale Steyn then deceived Will Jacks with a slower ball to leave Surrey 25 for 2 in the fourth over.
But Finch, back in the side after missing three games because of a family bereavement, continued his outstanding form in the Blast, taking his competition aggregate to 545 runs.
He had a reprieve on 18 when Lewis McManus dropped a regulation chance at deep mid-wicket off Liam Dawson. Otherwise Finch was untroubled as he and fellow Australian Nic Maddinson put on 92 for the third wicket in 11.4 overs.
Maddinson also had a life when he was badly dropped by Joe Weatherley at long on off the luckless Dawson on 31, but the pair took control thereafter with Finch depositing Gareth Berg over mid-wicket to bring up his fifth half-century in this season's Blast while Maddinson produced the shot of the night with a pulled six off Steyn that landed 30 rows back in the stand front of the gas holder.
Rahman picked up his second wicket when Maddinson was stumped aiming to leg but Surrey only needed 17 to win and Finch saw them home, his runs coming off 57 balls with seven fours.
Earlier, after deciding to bat first, Hampshire had been becalmed by a slow pitch and some disciplined bowling and their total of 133 for 7, which only contained two sixes and nine boundaries, was never likely to test Surrey's powerful batting.
They started promisingly. Rilee Rossouw and Sam Northeast took them to 49 for 1 in the sixth over but after Rossouw upper-cut a slower ball from Morne Morkel to point Hampshire struggled to pick up momentum.
Northeast battled through to the 19th over to top score with 37 but his runs came off 36 deliveries and only contained one boundary and whenever Hampshire attempted to accelerate they invariably lost a wicket.
Dawson briefly flourished before picking out short fine-leg trying to repeat a scoop off Morkel which had brought him a boundary from the previous ball. Captain Jade Dernbach picked up two wickets in the penultimate over and was the pick of the seamers with 2 for 19 while Batty also enjoyed the conditions, getting the ball to grip and turn as he took 1 for 18. Having been 77 for 2 at halfway, Hampshire only added 60 runs in the second half of their innings.