Ash Hunter's 65th-minute strike sealed a 3-2 win for Fleetwood over Bury - but only after Jermaine Beckford missed an injury-time spot-kick.
Fleetwood should have taken the lead in the 10th minute but after Amari'i Bell was felled in the box by Tom Aldred, Jordy Hiwula scooped the subsequent penalty way off target.
But Hiwula made up for that earlier miss with two close-range finishes as he diverted in wing-back Lewie Coyle's centre from the right in the 22nd minute and Bell's inch-perfect cross from the opposite wing five minutes later.
Fleetwood were rampant but their fragility on set-pieces continued to be their Achilles heel as Bury got themselves back in the game in the 31st minute.
Chris Maguire's corner from the right was flicked on by Michael Smith into the path of Beckford, who showed his class to whirl through the air and cannon home an overhead kick.
Fleetwood did not learn their lessons and Bury were level a minute before the break as Town failed to clear another Maguire corner, with substitute Josh Laurent bundling the ball home.
After an enthralling first 45 in the torrential rain at Highbury, there was just one goal in the second half as Hunter's effort took the points.
There was late drama, though, as Town substitute Wes Burns was penalised for impeding Aldred at the back post in added time but Beckford blasted the spot-kick over the bar.