Colchester took a third-minute lead when Ian Henderson poked a low shot past Owls goalkeeper Stephen Bywater from close range, after Steven Gillespie had pounced on Michail Antonio's error in the box and picked him out.
Wednesday were largely restricted to long-range efforts in the first half but Nile Ranger squandered a gilt-edged chance after 19 minutes when he sliced well wide with the goal at his mercy, after Antonio had fired across goal.
But Wednesday got back on level terms seven minutes after half-time through Miguel Angel Llera, who converted from close range after Colchester had failed to adequately deal with Chris Lines' free-kick from near the corner flag.
Madine headed over from Lines' free-kick soon after while Gillespie forced Bywater to save, as both sides went for a winner.
Jermaine Johnson fired inches just wide late on as Wednesday were held.