The Steelbacks posted 220 for eight from their 40 overs as Wakely made 85 off 100 balls and David Sales blasted 74 from 80 deliveries with Mark Turner taking a superb four for 38.
David Willey and Oliver Stone then took early wickets to reduce the Falcons to 19 for two before the heavens opened three overs before a result was possible.
Derbyshire won the toss and chose to field and they managed to dismiss Kyle Coetzer cheaply for nine when he wildly slashed Turner to Dan Redfern at point in the fifth over.
Turner then claimed a second wicket when Willey edged him to wicketkeeper Chris Durham to fall on 21, but Wakely hung around to reach 50 off 65 balls with Sales also completing a half-century off 59 deliveries as part of a fantastic third-wicket partnership of 152.
It was finally broken when Sales, making his return from injury, was bowled by Turner and three balls later, Rob Newton chopped the same bowler onto his stumps after making a single.
Steelbacks wicketkeeper David Murphy (12) launched Tim Groenewald to Derbyshire captain Wayne Madsen at mid-off before Wakely walked when he was caught and bowled by Groenewald three balls later. Con de Lange was then superbly run out by a direct hit from Madsen at mid-off after facing three balls without scoring.
David Burton (five) followed in the same manner in the final over thanks to a wonderful throw from deep extra cover by Australia international Usman Khawaja.
Chasing 221, Derbyshire should have lost Khawaja in the first over but he was dropped by Sales at second slip when he had yet to score, but Chesney Hughes was to depart for 16 when he smashed Willey straight to Burton, who was standing at deep square leg before Durston was trapped lbw by Stone for a two-ball duck.
With the Falcons on 19 for two, heavy rain stopped play at the start of the seventh over and it only increased in intensity, making any further play impossible. Both teams therefore earned a point from the match, although Northamptonshire will be left frustrated after putting themselves in a winning position.