It was a welcome return to form for 38-year-old Higgins who hadn't won a title for seven months and suffered a first round exit at the World Championship in April.
He won seven matches in Sofia, knocking out the likes of Shaun Murphy and Ronnie O'Sullivan before comfortably beating Robertson with top breaks of 60, 73, 118 and 82.
"It's a great start to the season for me, especially beating so many good players in one day," said the Wizard of Wishaw, who receives 25,000 Euros as well as 2,000 ranking points. "It gives me a lot of extra confidence.
"I'm playing with a new cue which I had made a few weeks ago. I wasn't sure if I'd like it at first because the chevrons are pointing towards the table rather than towards me as I've been used to in the past. But it's obviously working so far."
Earlier in the day, Higgins scored a 4-2 semi-final win over O'Sullivan, who had won five matches on his first appearance since his World Championship victory last month. Robertson edged out Crucible runner-up Barry Hawkins 4-3.
The tournament in the Bulgarian capital, which was staged for the first time last year with Judd Trump beating Higgins in the final, drew huge crowds, under-lining the popularity of snooker in continental Europe. "It's one of the best crowds we play in front of all season," Higgins added.
The European Tour comprises eight events, with the top 24 on the final Order of Merit to qualify for the Grand Finals next March, to be joined by eight more players from the Asian Tour Order of Merit. The next event is the Rotterdam Open from July 19-21.
Results (Last 16 onwards)
Neil Robertson 4-1 Anthony Hamilton
Jimmy Robertson 4-2 Anthony McGill
Scott Donaldson 4-1 Matthew Stevens
Nigel Bond 1-4 Barry Hawkins
Shaun Murphy 0-4 John Higgins
Stuart Carrington 1-4 Fergal O'Brien
Mark Williams 4-1 Sam Baird
Ronnie O'Sullivan 4-2 Mark Davis
Neil Robertson 4-2 Jimmy Robertson
Scott Donaldson 1-4 Barry Hawkins
John Higgins 4-2 Fergal O'Brien
Mark Williams 0-4 Ronnie O'Sullivan
Neil Robertson 4-3 Barry Hawkins
John Higgins 4-2 Ronnie O'Sullivan
Neil Robertson 1-4 John Higgins
Ball by ball scoring and results from tournaments