After starting with two group defeats, Wakely's highest List A score helped Northants to a first win, giving them three points from their last two games following a tie with Worcestershire.
They chased down Lancashire's 324-8 to triumph with 20 balls to spare.
Rob Keogh made 69 as the visitors reached 326-4 to win by six wickets.
He shared a key fourth-wicket stand of 152 with Wakely after Richard Levi (63) and Rob Newton had earlier put on 92 for the second wicket, while Adam Rossington weighed in with 20 off 12 balls at the end, finishing off the game with a six.
Despite four Lancashire batsman reaching half-centuries, Ryan McLaren (79), Jordan Clark (76*), Kolpak player Dane Vilas (61) and Karl Brown (58), Lancashire's third straight defeat leaves them now with a very tall order to qualify for the knckout stage.
They now travel to Edgbaston on Sunday to face Warwickshire, who have slipped below Northants to second bottom in the group.
Northants, who pulled off their best-ever List A run chase, go to Chester-le-Street to face Durham.
Lancashire's Jordan Clark told BBC Radio Manchester:
"It was a decent wicket and the collapse in the early overs wasn't ideal. It certainly put the lower order on the back foot. We had to rebuild without taking risks but, in the end, it wasn't enough. We were missing 30 runs.
"They put us under pressure in the Powerplay and they batted well all the way through. They took momentum into their batting and it worked out for them.
"We have a strong batting line-up but I don't think it's really clicked yet. We could score 400 really. The bowling has been off the boil but when you're hitting it well on a ground like this it becomes such a big total to defend."
Northants captain Alex Wakely told BBC Radio Northampton:
"We needed that win really. We have played some bit-part cricket this year and this was the first time we have managed to string it together with the bat.
"We weren't quite the finished article with the ball and we probably let them get too many from the position they were in. But it was a very clinical chase.
"It was an amazing start for us. Richard Levi set the tone but James Taylor has been big for us on making sure that someone is there at the end and that was my role. As a captain you want to be contributing."
Northamptonshire captain Alex Wakely led from the front with an unbeaten 109 to steer his side to a One-Day Cup victory over Lancashire in Liverpool.