Ugarte was the hero of the afternoon as Denis Smith's team won at Saltergate for the first time since 2000, whilst condemning the Spireites to only their second home defeat of the campaign.
The Dragons would probably have won even more convincingly but for an awful mistake by goalkeeper Xavier Valero, who was substituted at half-time as Michael Jones became the youngest keeper to represent Wrexham at the age of 17.
He was beaten by a Shane Nicholson penalty, but by then Ugarte had turned the game on its head.
Wrexham had been the better side, but when Valero raced from his line to be comfortably beaten by Ian Evatt's header, they looked set for another grim afternoon.
However Ugarte replied immediately with a header from 19 yards into the top right corner and then burst clear to hammer a right-foot shot past Carl Muggleton from 18 yards.
Ugarte was even booked before the break but he was quickly back in the spotlight with two more goals to seal Wrexham's victory.
Carlos Edwards, who had set up the first goal, again picked out the striker with a precise pass and Ugarte placed a low shot from 16 yards into the bottom right corner.
His fourth came after Chris Llewellyn flicked on a throw and Ugarte turned before curling a right-foot shot inside Muggleton's left-hand post.
Chesterfield threw everything at Wrexham and pulled a goal back when substitute Tcham N'Toya-Zoa was caught by Craig Morgan and Nicholson sent the young keeper the wrong way with a low spot-kick that found the bottom right-hand corner.
But it was too little too late for the home side and Wrexham deserved to complete a victory that boosts their chances of escaping from the relegation zone.