The goals scored against the run of play by Rotherham's strikers extended their winning run to five games, ending their opponents' four game winning streak.
Story of the match
Chiedozie Ogbene found himself in on goal for the visitors soon after, but his effort was straight at Bailey Peacock-Farrell. Luckily for the Irishman the flag was up for offside anyway.
Sam Hutchinson had a chance from a corner for Wednesday, but he headed over.
Nathaniel Mendez-Laing thought he was in on goal as he raced through on the left-hand flank, but he cut in only to fire straight at a Millers defender.
Josh Vickers was called into action for the first time in the game as he gathered a volley from Mendez-Laing.
Micheal Ihiekwe aimed a cross at the prolific Smith, but he was just unable to connect with it.
Ogbene then attempted to float the ball into Smith, but he was well marshalled by the Wednesday defence and could not hit the target with his header.
Massimo Luongo played the ball over the Rotherham defence trying to find Mendez-Laing, but he was not able to keep the ball in play.
The Englishman then cut in from the right-hand side having seen a lot of the ball early on, but his shot was easily saved by Vickers.
Wes Harding looked to be struggling under pressure from Callum Paterson, but the referee deemed the pressure from Paterson to be too much and awarded a foul.
Wednesday had the ball in the net in the 32nd minute only to see it ruled out, as Mendez-Laing found Marvin Johnson in the box, he lifted the ball above the Millers’ defence to Jack Hunt who slotted in from an offside position, which the linesman duly flagged for offside.
Ben Wiles made an important recovery challenge for Rotherham to prevent Bannan racing through on goal when the Wednesday captain seemed to be the favourite to win the race.
Bannan then had a shot from the edge of the box, which rolled wide.
Peacock-Farrell came off his line to clear just before the onrushing Ladapo could steal possession.
Liam Palmer managed to find himself in space after a powerful run, but his shot was blocked and the resulting corner came to nothing as the game approached half time.
The full back had another shot from range for Wednesday, but he could only force a routine save from the keeper.
The game was goalless at the break, in a half which The Owls were probably the better side, but there was still all to play for at the interval.
Half time score: Sheffield Wednesday 0-0 Rotherham United
Dan Barlaser made an important tackle to force a cross behind for a corner that that had the potential to threaten Vickers' goal.
Harding defended expertly well for the visitors to slow Paterson down in a two on two that allowed Vickers to collect the ball for The Millers.
Wiles had the chance to cross for Paul Warne's side, but the pass was wayward and Smith could get nowhere near it.
Paterson looked to capitalise on a poor clearance from Wiles, but his headed effort from a cross went over.
Harding was once again on hand for Rotherham to stop Mendez-Laing in his tracks after he skipped a few challenges.
The Millers took the lead against the run of play in the 59th minute through Ladapo.
A corner picked out Wiles, who headed goalwards and Ladapo was there to turn it in from close range.
Vickers made a crucial save to palm away a free kick from Bannan as Wednesday looked for a fast response.
Shane Ferguson made a vital interception to put the ball behind for a corner as Darren Moore's side continued to push for an equaliser.
Hunt then received the ball on the edge of the area but fired over.
There were appeals for handball from the home crowd as the game went into the final 10 minutes, as Bannan's shot hit Ihiekwe, but nothing was given.
Smith then wrapped the game up for Rotherham as he received the ball inside the box and curled it beyond Peacock-Farrell leading to scenes of jubilation in the away end.
Ogbene had the chance to rub salt in the wounds when his effort from range grazed the roof of the net on its way over.
Full time saw Rotherham secure a massive win in the context of their season, Wednesday had more than enough chances to win the game themselves but were not clinical.
Takeaways from the match
Whilst the majority of the chances went to the hosts, it was Rotherham who were able to dispatch the ball into the back of the net twice, as The Millers once again showed why they could be the champions this season.
They were nowhere near their best but were still able to fashion two openings which were all that was needed to secure a vital three points for Warne and his team.
Defensively the visitors were compact and were able to limit Wednesday to very few major chances despite having the majority of the ball.
The overall performance from Rotherham will have pleased Warne, as his side were still able to come out on top in a derby where they were under pressure against a Wednesday side who had won their last four before facing The Millers.
In contrast, Wednesday passed up on an amazing opportunity to come away with three points, as two lapses in concentration and the failure to take their chances proved costly to The Owls, who dominated large spells of the tie.
The performance from the hosts was hard to criticise, as Wednesday did show a lot of spirit in the way in which they played, however their end product and defensive lapses will be concerning to Moore.
It may well have been Ladapo who scored the crucial goal, but it was Harding's superb defensive display that spurred Rotherham on to victory.
The defender was able to secure his side a clean sheet in a game where The Millers' defence found themselves under pressure for large spells in the game.
Harding was particularly effective when it came to marshalling Mendez-Laing, who looked to be a major threat to Rotherham throughout the game.
Sheffield Wednesday: Peacock-Farrell, Palmer, Hutchinson, Bannan ©, Paterson, Byers, Johnson, Luongo, Hunt (Sow 78'), Storey, Mendez-Laing (Kamberi 83').
Rotherham United: Vickers, Harding, Barlaser, Wood ©, Wiles, Ladapo (Mattock 87'), Ogbene, Lindsay (Rathbone 45’), Ferguson (Osei-Tutu 79'), Ihiekwe, Smith.
Referee: Darren Drysdale