Swansea wingman Brad Maylett was the star of the show as the home side raced to an opening day success.
Maylett bagged the first hat-trick of his career and although Bury pulled goals back through Andy Preece and Lee Connell the Swans were deserved victors.
"I've taken a lot of stick as I haven't scored for five years," said Maylett.
"It was very hot out there and the hottest I've ever played in but the lads all kept going and we fully deserved the three points.
"I had set myself a goal target for the season but after scoring three today I might have to revise it slightly." Maylett opened the scoring after just four minutes when he side footed a James Thomas cross into the corner of the net.
Bury kept plugging away and veteran player-manager Andy Preece levelled the scores with a neat header in the 19th minute.
Neither side could profit from the few moments of goalmouth action and it was not until ten minutes from time when the players began to wilt that the goals started to arrive.
Maylett bagged his second in the 80th minute and when debutant Trundle was on hand to make it 3 -1 three minutes later the Swans looked home and dry.
Back came Bury and substitute Connell reduced the deficit in the 86th minute but Maylett had the final word when he completed the scoring in the dying seconds from a crossed shot from the edge of the area.
"It was important to get that first win and the manner in which we did it was pleasing," said Swans boss Brian Flynn.
"I told the players that the final 20 minutes would be crucial in the heat and so it proved but I knew our fitness levels were good and I had no doubt we would remain strong.
"We look capable of scoring a lot of goals but I am aware we have some weaknesses at the back but we will work on that during training."