League Two's second-bottom team made a mockery of the table as Ugarte ran riot in a brilliant attacking display.
There was some awful defending from both teams on a freezing afternoon, but Ugarte punished Pool for their schoolboy errors.
There were goals galore in a mistake-ridden first half, Spaniard Ugarte grabbing a hat-trick to send Wrexham in for the break ahead.
Wrexham's wall opened up obligingly for Gavin Strachan's free-kick to give Pool a third minute lead, but Ugarte levelled on 11 with a clever lob.
He gave them the lead with a close-range deflected shot on 20 minutes, but 10 minutes later Ritchie Humphreys headed the ball onto Joel Porter in the area to equalise.
But Ugarte was on the mark again with a penalty four minutes later after Eifion Williams pushed Chris Llewellyn in the area.
Sixteen minutes into the second half Pools were level as substitute Matty Robson raced down the left and pulled the ball back for top scorer Adam Boyd to hammer his 21st goal of the season from the edge of the area.
But Ugarte regained the lead for the visitors on 67 minutes, scoring from 12 yards after a good ball from Carlos Edwards.
Hartlepool were looking better than they had in the first half, and they levelled with seven minutes left as Porter grabbed his second from close range after two shots had been blocked.
Wrexham had their sights on nothing less than three points, though, and when they broke out on 85 minutes Mark Jones gave them the lead again.
With two minutes left Ugarte raced away to prod in Llewellyn's cross for his fifth, taking his tally for the season to 19.