Rhodes pounced on a defensive mix-up to tap home the opener, before defender Henley put Blackburn two up in the 26th minute.
Although substitute Chris Maguire pulled a goal back for Wednesday, the visitors won away in the league for the first time since success at Nottingham Forest on October 25.
Wednesday’s new Thai owner Dejphon Chansiri was introduced to the Hillsborough faithful ahead of kick-off, 48 hours after announcing at his first press conference his intentions to lift the club into the Barclays Premier League by 2017, the year it celebrates its 150th anniversary.
Chansiri, whose family owns Thai Union Frozen Products, confirmed he funded his recent £37.5million takeover from his own personal fortune – and there is a justifiable air of optimism about the club.
Wednesday striker Will Keane went close to increasing it in the fifth minute when his shot on the turn was smothered by Blackburn goalkeeper Jason Steele, but it was a low-key opening to the game and the upbeat mood was soon to turn flat.
Blackburn had steadily gone about their business and then cashed in on some dreadful home defending to take a 17th-minute lead.
Rovers striker Chris Brown’s header was allowed to roll between Wednesday’s last line of defence and goalkeeper Keiren Westwood, and the ever-alert Rhodes ran on to tap in his simplest finish of the season.
Westwood saved brilliantly to keep out former Owls loanee Ben Marshall’s header soon after and the same player’s subsequent corner bounced off the crossbar, while the Owls goalkeeper was powerless to prevent the visitors doubling their lead in the 26th minute.
Blackburn winger Chris Taylor slipped a clever pass into Henley’s path inside the area and the marauding full-back stabbed a low shot beyond Westwood and into the far corner.
Owls skipper Jose Semedo limped off with half-time approaching and was replaced by Maguire – but the home side did not threaten to redress the balance before the break.
Keane blazed a shot high over the crossbar soon after the restart as Wednesday toiled, but after Lewis McGugan’s superb free-kick finally troubled the Blackburn defence, the hosts pulled one back.
Maguire’s stinging close-range drive was blocked by Steele after Rovers had failed to clear the danger – and in the ensuing scramble Maguire slammed the ball home when given a second chance to make it 2-1 in the 61st minute.
Big Owls striker Atdhe Nuhiu’s shot was charged down and another blast from Maguire was heroically blocked as Blackburn, the first team this season to keep a clean sheet at Bournemouth on Saturday, tenaciously held on during five minutes of added time to take maximum points.