The Dane, who came into the week battling to save his card, fired eight birdies in a closing 65 to finish 20 under par in Vilamoura, four clear of Scotland’s Marc Warren.
The 26-year-old was never caught during the final round, and afterwards admitted he had been keen to take control of his own destiny.
“Today is up there with one of my best rounds,” said Bjerregaard on Sunday. “Not so much the six under around here, I’ve done that before, but under the pressure some of the shots I hit – the two shots I hit on 17 are some of the best I’ve hit in a long time.
“I felt like it was my time to go out and grab it and not wait for someone to hand it to me.”
Bjerregaard was a shot clear heading into the final round and holed a ten foot birdie effort on the first.
A lovely pitch to eight feet set up a gain on the fourth and he went back-to-back by getting up-and-down from a bunker on the par five fifth before holing from 25 feet on the eighth.
He overshot his approach to the ninth and then miscued his chip, with the subsequent bogey seeing his advantage halved as George Coetzee and Graeme Storm applied some pressure.
Back-to-back birdies at the tenth and 11th sent him clear again and, although Bjerregaard dropped another shot on the 14th after finding sand off the tee, he picked up his seventh and eighth gains of the day on the 15th and 17th to complete a commanding victory.
The display of front-running was all the more remarkable given Bjerregaard started the week 114th on the Race to Dubai Rankings presented by Rolex – only the top 100 keep their cards – and outside the top ten on the access list.
“It feels really good,” he added. “It’s definitely not been the year I’ve been looking for.
“To be honest it’s been really tough, so to be in contention again felt really good and to come out on top feels even better.
“I felt pretty confident. My girlfriend asked me this morning if I was nervous and I said: ‘no, don’t worry I’ve got this’, probably more to calm her down than anything.
“I’ve been in this position a couple of times before so to finally come through and get my first win feels really good.”
Warren, who came into the week down at 173rd on the Race to Dubai, boosted his chances of retaining his card with a closing 67 which gave him outright second when Coetzee found water at the last and ran up a triple bogey.
Storm and fellow Englishman Eddie Pepperell tied for third on 15 under, with home favourites Ricardo Gouveia and José-Filipe Lima a shot further back.