Hoilett put the visitors further ahead three minutes later, meeting Tomlin's low cross with a fine first-time finish.
Wednesday threatened when Barry Bannan's shot was well saved by Neil Etheridge and skipper Tom Lees pulled a goal back for the hosts in the 18th minute when his far post header from Bannan's corner went just inside Etheridge's left-hand post.
Harris said: "I'm very pleased. On the back of a very strong performance against Millwall, but without the end product in the final third, I thought today we had that end product in the first 15/20 minutes.
"The goals we scored were after some excellent play – the second one in particular was top level football and it was really good.
"We then had to deal with the adversity of two players coming off. We put Sol (Bamba) on, changed our shape and looked a lot more solid. I thought we deserved to see the game out as comfortably as we did in the end.
"I thought Sol was very impressive. When you've got senior players like that, you can rely on them.
"We've played some really good football and defended really well as a unit. We're a work in progress and I'll always demand more.
"We won't be spending any money in January. We're going to have to be clever and look at loan players or frees. I've got a strong group of players."
Lees went close to scoring an equaliser, seeing his initial shot blocked and then his follow-up cleared off the line by Leandro Bacuna.
A late challenge by Hoilett on Palmer resulted in the former receiving a yellow card amid strong protests from the home crowd, while the Wednesday player had to be helped off the field.
In stoppage time, Wednesday substitute Atdhe Nuhiu burst through the centre and shot wide.
Wednesday boss Garry Monk said: "They were poor goals to concede after we started really well.
"Against the type of team Cardiff are, you know how difficult they're going to make it.
"We responded with the one goal back and in the second half we pushed and we tried but with the set-up they had and the lead that they had, we couldn't quite break them down and unfortunately we couldn't quite get that equaliser.
"In the first half I thought we played some good football and opened them up a few times. Unfortunately, we just gave ourselves a little bit too much to do."
Commenting on Hoilett's challenge on Palmer, Monk said: "I don't want red cards for players but it's nothing other than a red card. It's reckless and it's out of control.
"Whether your feet are on the floor or not, I've got a player sat in the treatment room with an ankle the size of a balloon and if you can't see that from four yards away, as the fourth official was...
"It's either nothing or it's a red card. You'll have to ask them as I can't understand the decision."