Porta, which owns corporate and financial PR agency Newgate, had already invested at the beginning of the venture by Baiden and his former Red Consultancy colleague Nina Otero.
However, it has moved swiftly to take up its option to increase its initial 30 per cent holding to a 51 per cent controlling stake.
It had the option to do this at any time in the first two years but decided to accelerate its plans because of the new business record of Thirteen acting both by itself and in joint pitches with Newgate.
Porta said it paid £350,000 for the additional shares and will finance the deal by issuing 2.7 million new Porta shares at 13p per share.
Baiden said that the deal would give him more, not less, freedom to build Thirteen into a powerful consumer agency.
"Porta is putting PR at the heart of its growth strategy," he said. "This deal is an opportunity to grow the business and even look to overseas."
Porta group CEO David Wright said: "In September this year, Porta took a 30 per cent holding in Thirteen in exchange for start-up capital, including office-related costs, with an option to take a controlling interest over the next two years.
"However, after less than two months trading, the success of Thirteen in both new business brought in and in joint pitches with Newgate, prompted the decision to bring forward the group's plan for ownership."