The Owls managed the flow of the game perfectly, taking the lead through Callum Paterson, who punished a mistake from Chris Mepham to net his fourth goal in seven games.
Bournemouth, however, came out in the second period spritely, equalising through Junior Stanislas' penalty, but a smart Wednesday move in the final minute of the game ended with a bullet header from Rhodes.
Story of the game
The Owls started the game the better and had an excellent opportunity to take the lead in the opening minute of the fixture.
Barry Bannan won possession on the left before he backheeled the ball into the path of Adam Reach, who carried the ball down the channel before cutting it back towards the edge. Paterson dummied the pass, allowing Elias Kachunga to take the ball into his stride, however, his subsequent effort was saved by the outrushing Asmir Begovic.
Begovic was then forced into another superb save on 10 minutes, as a rifled effort from Bannan – situated just outside the area – needed to be tipped over the bar by the Bosnian goalkeeper.
After an emphatic start to the game, the next noticeable chance came on 26 minutes. Tom Lees was caught in possession by Junior Stanislas, who then played Lloyd Kelly into the area. The left-back found Arnaut Danjuma in the centre, but his effort was blocked by the last-ditch challenge from Sam Hutchinson, sending the attempt narrowly over the bar.
The hosts were slowly working their way into the game, however, they gifted Sheffield Wednesday the lead just before half-time.
Kachunga pressed Mepham on the right-hand side of the area, forcing him to play a careless and panicked pass across the area. The ball kindly rolled into the feet of Paterson, who placed his effort between the awkward dive of Begovic and the slide of Steve Cook.
Four minutes after the restart, Brooks had the second period’s first chance, curling a shot wide of the upright.
Bournemouth started the second half spritely, and almost found a way through a sturdy Owls backline. Stanislas floated a set-piece over the top and into the path of Sam Surridge, who mistimed his shot as the ball landed in the gloves of Westwood.
The Cherries were awarded a penalty on 67 minutes when Hutchinson hacked down Surridge in the area after managing to get goal-side of the versatile defender. Stanislas stepped up and powered home his ninth goal of the season.
Bournemouth intensified the pressure from the off, going close a minute later as Lewis Cook’s deflected strike forced Westwood into a fingertip save.
With 15 minutes remaining, Westwood again came to the rescue, saving from Brooks’ angled effort as he almost benefitted from Lees’ misjudged header.
However, Rhodes won the game for the Owls with a fantastic last-minute header as he powered home from Kadeem Harris' delivery from the right to end his 16-game goal drought.
The Cherries almost levelled in the final minute of stoppage time, as Jefferson Lerma saw his venomous strike pushed over by Westwood, but the Owls weathered the storm to pick up a vital three points.
Takeaways from the game
An outstanding effort from Wednesday
The Owls managed the game superbly, pressing Bournemouth from the off and forcing them into passes that they did not want to make.
This was how Wednesday got their opener, with Kachunga pushing Mepham into a lackadaisical pass across the area, allowing Paterson to convert.
The most pleasing thing for Owls fans was the way Wednesday not only pressed but played more expansively, as they were a lot more adventurous with their possession. When upsetting Bournemouth’s rhythm, they looked disjointed when Neil Thompson’s side attacked.
It was only when Wednesday sat back is when we saw the Cherries find space, but the response to the equaliser showed that there is still enough fight in this side in their bid for survival.
Bournemouth’s dreaded run
Fortunately, the Cherries remain in the top six, with a two-point gap between themselves and Middlesbrough, however, if Blackburn Rovers are successful in their game in hand then that could see them drop out of the playoff positions.
Jason Tindall’s side have the chance to turn their form around, facing teams in the bottom eight in their next five league fixtures.
Man of the match
Westwood was superb as the Owls grabbed a vital victory, continuing his impressive performances since his reintroduction to the side.
The Irish international made four excellent saves to keep the Cherries at bay, only being beaten from the spot after a mistake from Hutchinson.
Westwood’s experience could prove vital if Wednesday are to avoid the drop.