The 22-year-old Sydney-born midfielder netted the winner in the 80th minute as struggling Hamilton claimed a crucial three points to move away from the drop zone.
 
Earlier in the contest, fellow Aussie Trent McClenahan (who put in a full shift) had to clear Chris Maguire's goalbound header off the line.
 
And just before half-time, Wesolowski could've got his personal tally off the mark when he put a good chance wide.
 
But with the scores locked at 1-1 with ten minutes to go, Mickael Antoine-Curier sent the ball into Wesolowski's path and the Aussie drilled it in for the winner.
 
Hamilton boss Billy Reid commented after the game, "That was James' first senior goal, which is incredible because in training he is a great finisher but for some reason he has not managed to get on the scoresheet. I hope it is the first of many.''
 
Wesolowski, who is on a six-month loan at Hamilton from English Championship club Leicester City, is enjoying a good run in the Accies side after several injury-ruined years.
 
Elsewhere in the SPL, Scott McDonald had a quiet day against his old club Motherwell but provided the assist for the Marc-Antoine Fortune's winner as Celtic won 3-2.

And Danny Invincibile was back in action after a calf injury, playing a full game as Kilmarnock drew 1-1 with high-flying Hibernian.
 
Elsewhere around Europe's top leagues, in the Dutch Eredivisie, David Carney was an 84th minute sub as FC Twente retained top spot with a 3-1 win over NAC Breda. Nikita Rukavytsya wasn't involved.
 
Staying in the Netherlands, Brett Holman missed Dick Advocaat's first game in charge of AZ Alkmaar, which PSV Eindhoven won 1-0. Holman suffered a calf injury in the midweek Champions League game and wasn't fit for Saturday's game.
 
In the German Bundesliga, Dario Vidosic and Matthew Spiranovic were both absent as FC Nurnberg lost for their third consecutive match, 4-0 at home to Hamburg SV. Nurnberg are struggling down in second last in the Bundesliga.
 
In the Swiss Schweizer Pokal, injured Socceroo Scott Chipperfield watched on as FC Basel moved into the final four with a 3-1 win over Biel-Bienne.
 
In the Romanian Liga I, Joshua Rose and Josh Mitchell played full games as Universitatea Craiova lost 1-0 at Otelul Galati.
 
In European lower tier leagues, Carl Valeri was absent again for Grosseto as they won 1-0 at Piacenza in Italy's Serie B.
 
In Scotland's Division One, in-form Erik Paartalu provided the assist as Morton lost 2-1 to Queen of the South.
 
Elsewhere in Scotland's second tier, Ryan McGowan put in a full shift as Ayr United lost 3-1 at Dundee, while Simon Storey played a full game and Frankie Lagana put in an hour as Airdrie lost 5-2 to Partick Thistle.
 
Finally, in the Coupe de France, Ante Rozic's Sedan defeated Moissy-Cramayel 3-1 to move into the next round.