Windass opened the scoring early in the first half and Rhodes added a second in the 44th minute as Garry Monk's men produced a backs-to-the-wall display.
Wednesday had started the new season on minus 12 points after the club were found to have breached the English Football League's profitability and sustainability regulations.
Cardiff had a similarly troubled build-up after they sacked winger Nathaniel Mendez-Laing earlier this week in mysterious circumstances for what the club termed a breach of contract.
Neil Harris' Bluebirds paid the price for some sloppy defending and a lack of creativity even though they were more dominant in possession.
Monk's side put their points deduction behind them to move ahead in just the fourth minute. Cardiff's Leandro Bacuna gave away possession in midfield and Wednesday struck.
Izzy Brown played in Windass and the striker did brilliantly to race in on goal and finish smartly despite the presence of two covering Cardiff defenders.
Sean Morrison also headed a corner wide as Cardiff dominated the ball but failed to break down a resolute Wednesday defence.
Windass came close to a second when he forced Alex Smithies into an acrobatic save, but Wednesday did double their advantage before the break.
Barry Bannan's free-kick was flicked on by Windass and strike-partner Rhodes couldn't miss.
Kieffer Moore had gone close with the last action of the first half for Cardiff, who had 72 per cent of the possession, but they lacked fluency in midfield and a clear attacking threat.
Monk also replaced both his scorers but Cardiff's attacking substitutions couldn't make a difference as Wednesday stayed resolute and organised.
Away substitute Elias Kachunga had a weak header saved and then saw Morrison block another effort but Wednesday never looked like letting their lead slip.
Brown, Windass and Bannan all produced stand-out displays as Cardiff's inability to test away goalkeeper Cameron Dawson came close to painful.
Harris will know he has work to do as last season's play-off side are capable of much better than this.