First half goals from Matt Ritchie and Lewis Grabban saw Bournemouth take the points from Hillsborough on Saturday.
The Owls gave themselves too high a mountain to climb by conceding twice before the interval and despite taking control of much of the contest, the early damage proved decisive.
Jacques Maghoma did pull one back late in the game but it was too little too late for the hosts.
Following the midweek washout against Wigan, it was all change for Wednesday as injury dictated the absence of Glenn Loovens and Connor Wickham, which meant recalls for Miguel Llera and Jermaine Johnson.
Giles Coke was also introduced to the midfield in place of Seyi Olofinjana.
And the Owls started brightly, forcing the Cherries on the front foot through the early exchanges.
But just as Wednesday appeared to be on the brink of striking first blood, Bournemouth took the lead out of the blue with their first attack.
Ritchie advanced on goal from the angle and drilled a low shot part the despairing Martinez into the bottom corner.
Andrew Surman then forced a fine save from the young Argentinian with a goal-bound effort before the visitors doubled their lead on 27 minutes.
Grabban darted down the middle and cut inside to unleash a fierce near-post drive that flew past Martinez and into the Kop goal.
It was hard on the Owls, who had actually enjoyed more of the possession but lacked that creative edge in the final third.
But Wednesday needed a response before half time and Nuhiu tested Lee Camp with a glancing header, while Coke slammed wide after making space on the edge of the area.
It was much the same as the teams emerged for the second period, with the danger for the Owls the fact that Bournemouth could sit on their lead and hit on the counter.
And that is how events transpired as for all their dominance, Wednesday struggled to penetrate the Bournemouth backline.
Stuart Gray made a double substitution just past the hour, handing Andelko Savic a debut and thrusting Jeremy Helan into the action.
The Owls went on to ask more of the questions – Llera hit narrowly over from a set piece – before they finally hit gold 11 minutes before the end.
Helan swung a deep cross to the back post that Camp could only deflect into the path of Maghoma, who swept home from close range.
That triggered a late onslaught from Wednesday and although the ball rarely left the Cherries’ half, the South Coast side weathered the storm and held on for the points.
Owls: Martinez, Palmer, Llera, Roger Johnson, Reda Johnson, Lee, Coke, Semedo (Helan 66), Maghoma, Nuhiu (Savic 66), Jermaine Johnson (Mattock 80)
Bournemouth: Camp, Francis, Surman (MacDonald 86), Elphick, Arter, Grabban (Pitman 90), Daniels, Fraser (Pugh 72), Ward, Ritchie, O’Kane