An early goal from Mark Jones set them on the way and Lee Roche settled it with minutes to spare. Roche played 41 games for the Welsh club five seasons ago while on loan from Manchester Untied, but this was his first goal for the Welsh side.
Boston, bolstered by their string of new signings, had hoped for a better start but they had a torrid first half and were forced to change their playing pattern to subdue the midfield influence of Welsh playmaker Darren Ferguson.
Ferguson had an early corner headed out by Ben Futcher, who was a good match for Wrexham's tall central defender Dennis Lawrence in the air.
United's best early chance came when Brad Maylett floated in a corner that keeper Michael Ingham turned round the post and the second header was cleared.
Jones' goal came from another Ferguson corner which Shaun Pejic turned back for the young midfielder to curl home from 20 yards, leaving keeper Nathan Abbey stranded.
New boy Jonathan Walters might have added a second but headed wide from a Lee Roche cross.
Ferguson set up Andy Holt for a good header early in the second half, forcing Abbey to make a fine save at the back post.
On the hour mark Wrexham had a penalty appeal turned down when Walters raced up the line and saw his shot pushed out by Abbey, dropping just too far for Lee McEvilly to get a tough. The Wrexham striker went down under a push from Austin McCann as he tried to recover.
Walters, making a good impression as boss Denis Smith's new striker, later hit the post and again McEvilly could not get to rebound.
United were struggling and disappointing, making little of their few chances. Noel Whelan chipped over from a Maylett cross, giving Ingham an easy save and then Maylett wasted another opportunity firing a 30-yard shot straight at the keeper.
Roche settled it with a gift goal after Walters' miscued pass flew across the box to set him up at the back post.