Paratore had been on course to become the first player to win a European Tour event without making a single bogey since Jesper Parnevik at the 1995 Scandinavian Masters.
The 23-year-old's brilliant run finally came to an end on his 63rd hole of the week.
But his closing round of 68 in testing conditions at Close House was enough to keep Hojgaard at bay.
In one of the first European Tour events after nearly five months of inactivity due to the coronavirus, Paratore's fellow players formed a socially-distant guard of honour behind the 18th green and he was surprised with a FaceTime call with his mother Cristina.
"It was really amazing," Paratore said. "I did not expect that from my friends on the Tour and it was a really good situation. I loved it and also to see my mum was a lovely surprise."
Paratore, who won the Nordea Masters in 2017, added: "This one feels amazing. I am really happy. I did not expect to come back and win so soon after lockdown but I have worked really hard the last year."
Paratore's one-shot overnight lead was wiped out by playing partner Justin Harding's birdie on the third, but the South African then completely mishit his tee shot on the next and came up 30 yards short of the green, from where he was unable to save par.
Paratore had three-putted the short third for par after a lucky bounce from thick rough saw his drive find the green, but he bounced back to hole from 20 feet on the fourth and extend his lead to two shots.
Paratore's first blemish came on the difficult ninth, where tournament host Lee Westwood had earlier run up a quintuple-bogey eight, but he produced the perfect response to birdie the next to briefly move three shots clear.
Another bogey on the 11th gave the chasing pack hope, but they were unable to apply any pressure and Paratore made certain of victory with a birdie on the par-five 17th.
Harding finished alone in third after a closing 72, with the English trio of Andy Sullivan, Robert Rock and Dale Whitnell sharing fourth place on 13 under.
Leading final round scores in the British Masters at Close House Golf Club, Newcastle, England, on Saturday (GBR/IRL unless stated, par 71):
266 - Renato Paratore (ITA) 65, 66, 66, 69
269 - Rasmus Hojgaard (DEN) 66, 67, 66, 70
270 - Justin Harding (RSA) 69, 63, 66, 72
271 - Robert Rock 69, 66, 67, 69; Andy Sullivan 68, 69, 67, 67; Dale Whitnell 68, 64, 68, 71
272 - Oliver Fisher 65, 69, 70, 68
273 - Ryan Fox (NZL) 67, 67, 71, 68; Jonathan Caldwell 67, 69, 67, 70
274 - Ben Stow 67, 68, 68, 71; Jens Fahrbring (SWE) 68, 69, 68, 69; Sam Horsfield 70, 70, 61, 73; Graeme Storm 71, 69, 67, 67
275 - Jeff Winther (DEN) 70, 67, 72, 66; David Horsey 70, 69, 68, 68; Ashley Chesters 67, 66, 68, 74