Atalanta began positively at the New Balance Arena, but Parma grew into the contest and took the lead through Fabbian's 41st-minute header from a Vincent Sierro corner.
The visitors doubled their advantage two minutes after the restart when Zappacosta diverted El Bilal Touré's cross into his own net. Lontani then completed the scoring in the 58th minute with an excellent right-footed finish from the edge of the penalty area.
Gilardino was delighted with the response from his players, particularly after the difficulties they experienced during the opening period.
"I'm happy for the players and the team. I had asked them to have faith in these players," the Parma coach said. "We suffered against Atalanta in the first half, but after taking the lead we saw a Parma who were more determined mentally and in their play."
The visitors' defensive discipline was equally important, with Gilardino highlighting the collective sacrifice required to keep a clean sheet.
"There was great sacrifice from everyone, and the fundamental thing was not conceding a goal. You need balance even when you win. The defeats that have come have forged this group and made it stronger."
Parma created several opportunities beyond their three goals, something which particularly pleased their coach.
"We defended well and created many chances, in addition to the three goals. It is fundamental for us to have an awareness of our potential. I believe very much in this group," he said.
Gilardino also singled out Sierro and Hans Nicolussi Caviglia, while praising Fabbian's development and his contribution in midfield.
"Fabbian is a player I have wanted to have in my team for a long time. He can do more, but I am happy with his growth in terms of managing the ball and his contribution in midfield," he explained.
"I also want to highlight the good performances of El Bilal Touré and Lontani. The priority is always to remain compact."
Atalanta coach Maurizio Sarri was considerably less satisfied, describing the defeat as difficult to explain after his team's promising first-half performance.
"We conceded just before half-time and made the mistake of returning with the wrong emotional attitude. We paid a heavy price for that," Sarri said. "The numbers do not justify these results. We must apologise to the club and the supporters, stop listening to everything outside and rediscover our unity."
The coach insisted the problem was not simply tactical.
"We lost this match mentally and emotionally, regardless of the tactical aspect. We had a very good first half, but what happened afterwards was not about tactics. It was about character."
Sarri also criticised his team's lack of ruthlessness in decisive moments.
"We create several promising situations that we should turn into goalscoring opportunities, but we struggle to execute. We lack aggression at key moments."
The Atalanta coach admitted his side had conceded too many avoidable goals and needed to improve quickly.
"These are goals we should not be conceding. We have to improve."
Parma, meanwhile, will take considerable encouragement from a performance which combined attacking efficiency with the defensive organisation Gilardino had demanded.