Sheffield Wednesday were forced to settle for a third draw in their last five games as they were unable to capitalise on their control of the game against Gillingham.
Oliver gave the visitors an unlikely lead after 21 minutes despite a fast start from the Owls with a cool finish past Wildsmith.
It was not until the 75th minute that Kamberi had provided the hosts with the equaliser their performance deserved, but Darren Moore's side had the chances to leave with all three points on the day.
Story of the Match:
The Owls dominated the early stages of the game, as Kamberi had the hosts' first shot six minutes in but could only fire at Cumming in the Gillingham net. Shodipo's early sighter from range went over the bar soon after.
Paterson was desperately unlucky not to put the hosts in front when he flicked the ball onto the post from a cross which left Cumming unmoved.
In the 21st minute Gillingham had the lead against the run of play, when a flick on found Oliver in acres of space, and he was able to slot the ball past Wildsmith into the bottom-right hand corner.
Paterson broke forward for The Owls looking to equalise, but his pass couldn't play Shodipo in on goal.
There were appeals for a penalty for Darren Moore's team around the half an hour mark, as Bannan's headed effort was alleged to have hit a defender's arm on its route wide, but the referee waved away the claims.
O'Keefe's effort from range crept just wide of the right-hand post, as Gillingham seemed content to shoot from range to catch out stand-in goalkeeper Wildsmith. He replaced Peacock-Farrell for The Owls, who is away on international duty with Northern Ireland.
Akehurst made a vital block just before the break to keep The Gills in front, deflecting a Corbeanu shot aimed for the back post away from goal.
Despite Sheffield Wednesday's strong start, it was The Gills who led at the interval. Steve Evans' team still had work to do to if they were to see out the victory, but Oliver's effort was the difference between the two sides at the break.
Half time score: Sheffield Wednesday 0-1 Gillingham
Corbeanu's cross into the box was past Cumming leaving an empty net, but there was nobody on the end of the pass to level the score line for Wednesday.
Corbeanu tried again from range, but his shot was straight at Cumming. The winger had a real lack of options after completing his driving run, which led to him taking the shot on.
The home crowd became more frustrated as the game developed with alleged time wasting from the Gillingham players, with Dempsey and O'Keefe receiving treatment in the early stages of the second half.
Paterson squandered a huge chance to equalise for Wednesday when he received the ball from a cut back from Corbeanu, only to put his shot wide from just outside the 6-yard box.
Two minutes later substitute Berahino received the ball in a dangerous area, but he could not quite bring it under control, which prevented him from having a one-on-one against Cumming.
With 15 minutes to play Kamberi had the leveller for The Owls: Bannan's shot was parried away by Cumming but only as far as Kamberi, who had a simple tap in to make to 1-1.
Tucker was on the line to hook the ball away in a vital clearance for Gillingham that would've seen them go from winning to losing within two minutes had Tucker not been there to stop a cross turned shot that had Cumming beaten.
Full time saw Gillingham end the game the happier of the two sides despite having taken the lead. Moore's side dominated the opening and closing 15 minutes of the game and probably should have had more to show from those periods in control of the tie.
Sheffield Wednesday: Wildsmith, Palmer, Dunkley, Johnson, Corbeanu, Dele-Bahiru (Adeniran 90'), Bannan, Wing (Berahino 61'), Shodipo (Sow 82'), Paterson, Kamberi.
Gillingham: Cumming, Jackson, Tucker, Ehmer, Akehurst (Adshead 72'), Phillips, O'Keefe, Dempsey (Reeves 74'), Lloyd, Akinde, Oliver (Sithole 56').
Referee: John Busby