The defending champions stunned the ladder-leading Hobart Hurricanes in Launceston on Thursday, chasing down the hosts’ target of 170 with 13 balls to spare.
Weatherald smacked 82 from 42 balls with an incredible strike rate just under 200, while Carey hit 54 from 35 to breathe new life into the Strikers' season.
In pursuit of Hobart's 7/169, the openers combined for a century stand that included 86 runs off the first six overs.
Weatherald had a reprieve on 30 when he was dropped by Jofra Archer at mid-off.
Carey was dismissed caught-and-bowled by Simon Milenko in the 10th over and Weatherald holed out three overs later but by then the damage had been done.
Jonathan Wells (19 not out) and stand-in skipper Colin Ingram (two not out) guided the Strikers home.
The seven-wicket win means the Strikers are just two points behind the Melbourne Stars in fourth spot and remain a chance of making the finals with two games to play, pending other results.
The Hurricanes posted 7/169 after being sent in to bat at UTAS Stadium, with skipper Matthew Wade top scoring with 88 off 54 balls.
Hobart looked on track for a massive total in front of a home crowd of 13,846 but stumbled late, losing 5/19 within the final four overs.
Ben Laughlin (3/31) was the pick of the Adelaide attack against his former side, while Afghan spinner Rashid Khan and Michael Neser picked up two wickets each to put the brakes on the in-form Hurricanes.
Wade combined for a 59-run stand with D'Arcy Short, who was caught at cover off Laughlin for 26 from 19 balls.
The Hurricanes, who are a win clear atop the table, have now lost two of their past three matches.
The Strikers play their final two home and away matches at Adelaide Oval against bottom-two teams the Brisbane Heat and the Perth Scorchers.
Tickets to Sunday’s clash with the Heat are still available.