Jordan Rhodes added a fourth in the 65th minute and Reach rounded off the scoring with his second of the match.
Paterson scored a fine goal in the 20th minute to put Wednesday further ahead, meeting Liam Palmer's cross with a superb first-time finish.
Reach added a third three minutes later, firing into the top right-hand corner of Phillips' net following a free-kick.
Rhodes made it 4-0 after Bannan released Paterson on the right and his low cross was swept home by the striker.
Reach scored his second of the match in the 69th minute following Josh Windass' pull-back.
Smith, leading Wednesday in the absence of manager Darren Moore who tested positive for Covid-19 last week, said: "It was outstanding, both with and without the ball.
"To score five great goals and also some great defending as well, putting our bodies on the line, to keep the ball out of the back of the net.
"We know that we've got quality within the group and a performance like that is in them, it's just bringing it out more often.
"The players have set the standards. They have definitely got the quality to play like that consistently.
"There is real quality there and we have seen that from day one. Hopefully we will carry that on for the rest of the season. The clean sheet was just as pleasing as the goals.
"There are still seven games to go and we will continue to fight for every single point."
Cardiff boss Mick McCarthy said: "We seemed to have got dragged about with players out of position. We've not really done our jobs as well as we've done in the past and it's cost us.
"I have to say with the second goal, I'm not sure what we could have done about that.
"Having spanked it across to the wing-back and he spanked it back into the middle, Paterson puts it in. I don't know what we could have done to stop that. I almost had to applaud it myself – that's how good it was.
"I think we've been punished because we're pressing to get a goal back. We've been done on the break twice, which is disappointing. Under normal circumstances, I don't think that happens.
"It's a humbling lesson. It happens. Today was a bad performance by us. We'll just keep going and we've got to repair the damage emotionally as much as anything."