The Argentinian striker struck his first goal since his summer move from Estudiantes as Wigan manager Roberto Martinez secured victory over his former club Swansea at the DW Stadium on Tuesday night.
Cedric van der Gun should have given the Championship visitors an early lead but Boselli put Wigan ahead in the 51st minute and Ben Watson added a late penalty.
Victory was not as comfortable as the Premier League hosts would have liked but Swansea, backed by a vociferous 5,000-strong travelling faithful and buoyed by their rise to third in the Championship, made life difficult throughout.
The outcome could have been different had Van der Gun shot when clean through instead of opting to pass to an offside Craig Beattie in the best move of the first half.
The match was delayed by 15 minutes due to an accident on the M6. That gave the majority of the large Swansea following to have made the 230-mile journey time to take their seats.
And, as anticipated, they were soon in full voice, directing their ire and 'Judas' chants at Martinez over his acrimonious departure from the club last year.
Martinez's side, featuring fit-again captain Gary Caldwell for the first time this season in one of seven changes, were the first to threaten.
Mohamed Diame charged forward but the ball got trapped under his feet and Yves Ma-Kalambay was not troubled by his shot.
Swansea almost produced the perfect response and they should have claimed the lead as Darren Pratley sent Van der Gun away with a superb ball.
The Dutchman looked certain to score as he closed in on the restored Ali Al Habsi but strangely opted to pass across goal to Beattie, who was flagged offside before turning the ball home.
Victor Moses almost made Swansea pay with a tricky run down the left but his final ball was deflected behind.
Former Celtic striker Beattie almost got another chance after a good run from Pratley but the ball came at him too quickly and Al Habsi was not troubled.
Swansea enjoyed a good spell with Kemy Agustien having a shot blocked and Pratley winning a free-kick after catching out Antolin Alcaraz, who was booked.
Former Wigan midfielder David Cotterill failed to make the most of that opportunity before Jordi Gomez drove a set-piece into the wall at the other end.
Watson threaded a good ball into the Swansea box for Boselli, making his first appearance for a month, but Ma-Kalambay cleared.
Cotterill caused Wigan problems with a strong run but tried to beat too many players and the hosts cleared.
Wigan were again fortunate when Beattie was hacked down by Diame on the edge of the area but again Wales international Cotterill was wasteful from the dead-ball.
Wigan began to take greater control of possession at the start of the second half but initially still found it hard to find a way through a determined Swansea side.
The chance they had been waiting for finally arrived six minutes after the restart as Alcaraz split the visitors' defence with a superb through-ball.
Boselli raced through and calmly rounded Ma-Kalambay for a well-taken goal.
That strike appeared to fill the Argentinian with confidence and moments later he fired over when well placed before missing an easy chance for a second by heading wide from a corner.
Wigan had taken the ascendency and Maynor Figueroa tested Ma-Kalambay with a rasping drive from 30 yards.
Boselli, looking ever more dangerous, tried his luck from 40 yards after spotting Ma-Kalambay off his line and forced the Belgian to scramble back and concede a corner.
Boselli was withdrawn after 77 minutes as Wigan started to wind down towards the final whistle.
Swansea battled on but Van der Gun was unable to make the most of a Stephen Dobbie cross in front of goal.
The visitors were stretched again when Moses burst clear but Franco di Santo lost possession.
Wigan applied the finishing touch in injury time after substitute Charles N'Zogbia was tripped in the area by Andrea Orlandi and Watson struck from the spot.