Goals from Craig Bryson. Chris Martin and Richard Keogh put Derby in control before Grant McCann converted a penalty after goalkeeper Frank Fielding was sent off in the 61st minute.
Garner said: "We were totally in command as soon as the first whistle went. The first 20 minutes we were absolutely superb, dominated the game and were in their half constantly.
"We didn't get the goal our play justified but we stuck at it and when it came, it was a brilliant goal, a training ground goal really. Great hold up play from Conor Sammon and a typical Craig Bryson run and a good finish."
Garner had no complaints about Fielding's sending-off and admitted: "At the time I thought his starting position was too deep and I think he hesitated which was disappointing because the last thing we wanted was a penalty and a sending off. It was a poor decision by Frank, not the referee who got it spot on."