A super display by Lee Trundle, who took his goal tally for the season to five, helped the Swans secure their third successive win as Brian Flynn's side moved to the top of the Nationwide Division Three table.
"We could have scored more but after going two up we were a little sloppy defensively and they could have got back into the game," Flynn said after the comfortable victory.
"We had to be patient because they are a hard team to play against but we got the breaks in the second half.
"What you get with Lee Trundle is that when he is on fire he is red hot and besides his goal and near misses it was a great pass to Andy Robinson for our third goal.
"We needed a good solid start to the season and you can't do better than three wins out of three." It was four minutes into the second half when a rising drive from Trundle beat Paul Bastock in the Boston goal and ripped high into the net.
Three minutes later the Swans doubled their lead when Kevin Nugent headed a rebound off the crossbar into the far corner of the net.
Neil Redfearn almost brought Boston back into the game when he sent a 20-yard screamer against the crossbar with Brain Murphy beaten but Swansea were on a roll and substitute Robinson raced onto Trundle's flick for the third in the 86th minute.
"We didn't take our chances, particularly just after they scored their second, but overall we played pretty well in the first half," said Pilgrims boss Neil Thompson after the match.
"We created a fair share of goalscoring opportunities but it's also what happens at the other end that counts and we didn't keep a clean sheet."