In a dramatic Serie A encounter at Stadio Luigi Ferraris, it was Brozovic who had the final say with a crisp finish in the 94th minute.
Earlier drama had come courtesy of the VAR, which disallowed Radja Nainggolan's first-half effort before ruling out Kwadwo Asamoah's thumping strike in the 88th minute, then Gregoire Defrel's attempt at the other end a moment later.
But, in similar fashion to Matias Vecino's last-gasp winner against Tottenham in the Champions League on Tuesday, Brozovic stepped up to secure a much-needed triumph, and Inter boss Spalletti - who was sent off for an overzealous celebration - insists Inter proved their grit.
"This way of winning shows the character of this team, which keeps fighting for every ball and stays in the game," he told DAZN .
"It might mean taking a few risks, but we are Inter and we must always live on the edge to get a victory.
"Seeing this passion gives me greater strength to go forward and I'm glad that element is here rather than the tactics, as those will come with time.
"We took this issue of character to each and every player individually to make sure it was absorbed the right way."
Like many of Inter's star players, Brozovic has endured an underwhelming start to the campaign, but kept his composure when it mattered.
And the midfielder, who played an integral part in Croatia's run to the World Cup final, believes Inter have now turned a corner with what is just their second Serie A win of the season.
"It was a difficult game, but once again we won at the last gasp and we're happy. We must continue like this, getting the results," Brozovic told DAZN .
"We got a lot of passes wrong in the first half, but then we improved. I think this week will be the turning point in our season.
"They are all important matches and we've got to win them all, because that’s what Inter do."