The Steelbacks suffered a five-run reverse at the County Ground, losing for the second time in four Royal London One-Day Cup matches.
Durham made 256 for seven from their 50 overs with Rory Kleinveldt (2-50) and Graeme White (2-46) among the wickets for Northants.
The Steelbacks then endured a difficult start to their reply, losing Josh Cobb (6) and Ben Duckett (2) cheaply.
But they rebuilt steadily thanks to 79 from Wakely and 66 from Adam Rossington.
However, when both of those batsmen departed, Northants were up against it.
Rory Kleinveldt's quickfire 41 gave them hope, but the South African all-rounder was bowled with four balls remaining, and Northants needing 10 runs.
Final-wicket pair Nathan Buck and Ben Sanderson were unable to find the runs required and Durham celebrated a narrow success.
The defeat leaves Northants sixth in the Royal London One-Day Cup North Group table with four games remaining.
They head to Edgbaston for a televised clash with Warwickshire on Wednesday (start time 2pm).
And Wakely said: “We weren’t quite on it today from the start.
"We were a bit sloppy in the field, a few chances went down and a few too many runs were scored at the end of the innings to get them a good score on a slow pitch.
“And then we never really got into it batting.
"We lost early wickets, clawed our way back into the chase, but never really got on top of them.
“Nothing really clicked for us from the start and we now have it all to do this week.”