With both sides hotly tipped for promotion from their respective divisions this season, and both facing lower-league opposition, United and Cardiff went into their clashes as favourites.
And the Welsh side, relegated from the Premier League last year and targeting an immediate return, justified that tag as they triumphed 2-1 over Coventry City at Sixfields.
Finalists in 2012, Cardiff took an early lead as Guido Burgstaller struck in the fourth minute after Coventry had failed to clear their lines.
They doubled their advantage nine minutes from time when Ryan Haynes diverted the ball into his own net following Mats Moller Daehli's dangerous cross from the left.
Haynes was then involved at the other end as he teed up Shaun Miller to score, but Steven Pressley's side were unable to force an equaliser.
At Bramall Lane, Sheffield United needed a late winner from Marc McNulty to see off League Two Mansfield Town 2-1.
After a goalless first half, Andy Butler bundled home the rebound following Sascha Studer's save from Jose Baxter's header in the 53rd minute.
Mansfield were level four minutes later as Alex Fisher turned the ball home, but United won it four minutes from time as McNulty shrugged off the attentions of two defenders and slotted the ball past Studer.
