Martina grabbed their son Alessandro, aged 5, and rushed both children to safety but Gulotta, aged 35, was killed instantly.
Gulotta worked as a salesman in a computer shop in Legnano in northern Italy.
The Italian foreign ministry said three other Italians were injured in the attack. Two were discharged from hospital and the third was being treated for multiple fractures.
Mr Gulotta, from Italy, was beloved by his colleagues at Tom's Hardware, who said they envied his work-life balance and that everyone in the company knew who he was.
His colleague wrote on a post on the company's website: "He had posted on Facebook the stages of his journey and everything seemed to proceed as one would expect from a vacation trip.
"A photo from Cannes, one of the Ramblas in Barcelona. And then what no one expects: the death of a young man, father and life partner of the mother of his children."
His friends, family and colleagues found out on Wednesday night that Mr Gulotta had been killed in the attack.
The father-of-two worked in marketing and sales at the company.
A colleague wrote of him: "He was able to lead a rich family life and a brilliant professional career with a balance- and that I will always envy him."
His colleague said his heart was going out to the children, "little Alexander, who is preparing to start elementary school with the awareness that his life and family will no longer be the same.
"And then we think of the little Aria, who does not have the horrible scene in her eyes but will never know her dad. "
At least 14 people were killed and more than 100 injured in a terror attack on Barcelona's Las Ramblas on Thursday.
At least 24 different nationalities were among the dead and injured, officials said early on Friday morning.
A spokesman for Spain's civil protection had earlier said said that among the victims in the popular seaside city were nationals from France, Germany, Spain, the Netherlands, Argentina, Venezuela, Belgium, Australia, Hungary, Peru, Romania, Ireland, Greece, Cuba, Macedonia, China, Italy and Algeria - without detailing whether he was referring to those who died or were injured.