South African halfback Cobus Reinach scored two tries in an action-packed second half while former Blues five-eighths Piers Francis added to Dan Biggar's goal-kicking feats by landing two penalty goals.
Gloucester were competitive with rising Welsh wing Louis Rees-Zammit scoring a hat-trick of tries.
"When you've got backs who can score and forwards who never stop working to recycle ball for them, you can't ask for much more," Boyd said.
"It was a great occasion at the Gardens again, just like this time last year when we beat Exeter.
"We were obviously pleased to come out on top, although as the score indicates, it was a pretty close game," he told media afterwards.
Boyd said the side put their European losses to Leinster, and last week's Premiership loss to Sale, behind them.
"We were disappointed at Sale last week. But there was no correlation around those matches and this one. We didn't beat Gloucester at all last year so we're really pleased to do that. We go into the New Year in a reasonably good space," he said.
Northampton's win denied Bristol the lead in the competition when they were beaten 21-26 by Wasps.
Coach Pat Lam saw his side lose in the last minute when Nizaam Carr scored in the corner to claim the win for Wasps.
"We let a lot of people down," Lam said.
"It is extremely disappointing obviously, you know it's the second time in a row with the London Irish game that we have the game in our hands with a couple of minutes to go and we've blown it.
"The biggest disappointment is for our fans, our community, the people coming today, our fans around the world who are Bristol supporters, you know to put them through that, at the end is disappointing, and we are as a team.
"We let ourselves down and we let them down," he said.
Glasgow coach Dave Rennie saw his side go down to rivals Edinburgh 19-29 to reverse their 16-20 loss of a week earlier. The sides were contesting the 1872 Cup, and the holder will be decided in their third game to be played in May, 2020.