Brooks attempted an early curling effort from distance which went well wide.
Adam Reach had Wednesday's first chance, seeing his shot from a promising position take a deflection wide.
Liam Palmer had an even better opening for the hosts, heading wide after stooping to meet Bannan's free-kick before Josh Windass then put an angled shot over and Kachunga headed wide from a Kadeem Harris cross during a good spell for the hosts.
Windass went close again with a free-kick which just cleared the bar.
Danjuma fired in a 20-yard shot early in the second half but it was straight at Wildsmith who made an easy save.
King then threatened on the right-hand side of the area, putting a low ball across the face of goal, but there was no-one on hand to apply the finishing touch.
Brooks had a great opportunity to score when the ball fell to him after Wildsmith blocked King's effort, but Julian Borner came to his side's rescue with a vital challenge to divert the shot wide.
Kachunga put a glancing header just wide following Bannan's corner.
King then headed narrowly wide at the other end after connecting with an Adam Smith cross as the visitors pressed for the opener.
But Wednesday were awarded a penalty when Windass was bundled over in the area by Cook, who was sent off as a result, with Bannan converting from the spot in the 71st minute.
Palmer made a vital interception to thwart King, whose header from the resulting corner was clawed away by Wildsmith.
Substitute Callum Paterson had a chance to extend Wednesday's lead late on, firing straight at Asmir Begovic after getting on the end of a through ball from Bannan.
Harris was shown a red card in stoppage time for what appeared to be violent conduct.