Connor Wickham and Massimo Luongo scored from corners as Sheffield Wednesday dented Bristol City's play-off hopes with a 2-1 win at Ashton Gate.
The Owls, who had won only two of 15 games coming into the match, took a 13th-minute lead when Wickham rose unmarked to head home Jacob Murphy's corner, and doubled their advantage on the hour mark when Luongo bundled home another.
Bristol City gave themselves hope when Nahki Wells' header halved the deficit nine minutes later, but struggled to create anything to threaten an equaliser and are now seven games without a win.
That leaves the Robins five points off the play-offs with seven games to go, while Sheffield Wednesday eased any worries over their Championship future to move 10 points clear of the relegation zone.
Owls ease drop fears at Ashton Gate
Much-changed Bristol City looked to justify Lee Johnson's decision to shake up his line-up by flying out of the blocks and coming close to an early opener when only Joe Wildsmith's reaction save kept out Nathan Baker's point-blank header from a corner.
Sheffield Wednesday survived another close shave when Wells failed to connect with Jack Hunt's free-kick when even a glancing header would have likely sealed the opener.
The Owls gave their hosts no such reprieve when they forged their first chance, however. A training-ground move from a corner saw two defenders block off Nathan Baker, leaving Wickham a free run to the near post where he headed inside the far post.
The hosts struggled to impose themselves on the rest of the half, and had more trouble after the break when Baker had to atone for his early error to keep out a certain second, sliding in to block Rhodes from slotting in from six yards.
He could do little moments later, however, as another corner was flicked goalwards by Wickham, and when his effort was blocked Luongo reacted quickest to stab home from close-range.
Cruising Sheffield Wednesday suddenly looked nervous nine minutes on, when Wells nodded in the rebound after Wildsmith had kept out Baker's initial header.
But only a late miss from substitute Zak Vyner gave them anything to worry about - as the Owls picked up their first away win since January.
Man of the match - Barry Bannan
Bannan controlled the game from midfield for Sheffield Wednesday and made an impact at both ends of the pitch, completing more passes (43) than anyone else on the field while also winning possession back 15 times - also the most of any player.
"He's taken control of the tempo of the game, he never misplaces a pass, put in good defensive work, and had an all-round good game," said Sky Sports Football co-commentator Don Goodman.
What the managers said...
Bristol City's Lee Johnson: "It's so disappointing because I felt our performance was an improvement and that we deserved something from the game. But to concede twice like that from set-pieces was unforgivable. You can't hope to win games at this level if defenders don't do their jobs.
"If one is blocked at a corner, there needs to be enough communication for another to react. But that didn't happen with the first goal. The second was equally frustrating because we had chances to clear at the near post before the ricochet that led to the chance.
"The changes worked and we looked more threatening. There were some decent opportunities for us to score more than one goal. Their first goal was against the run of play because we started well. What we lack is a Barry Bannan-type player to pull the strings for us in midfield. I still believe we can go to Nottingham Forest and win our next game, but not if we defend like that."
Sheffield Wednesday's Garry Monk: "The players deserve huge credit because they have come back from the enforced break with a fresh attitude and mentality. It started in the draw with Nottingham Forest and today we looked solid defensively and threatening going forward. We can only focus on things we can control and I sense the start of the culture change I was talking about as being needed before the season was interrupted.
"We needed a fresh attitude and mentality because we were letting ourselves and our fans down. The players have had time to reflect and work on their fitness. It is only a couple of steps forward, but I have been really pleased with the last couple of games. No one is getting carried away because there is a lot of work still to do. But the signs are good that the players are taking on board what we want from them."
Both sides are back in Championship action on Wednesday night. Bristol City head to Nottingham Forest for a 6pm kick-off, while Sheffield Wednesday host West Brom at 7.45pm.