Tasos Douvikas rattled home the only goal of the game in the 71st minute at the Stadio Marcantonio Bentegodi as Como guaranteed themselves at least a place in the Conference League.
Como have never played in European competition in their history and were in the third tier of Italian football when acquired by tobacco giant Djarum in 2019.
The lakeside outfit were only promoted to Serie A in 2024 and could yet finish the season in the top four.
“Two years ago today we were promoted to Serie A and today we’re qualifying for Europe," said coach Cesc Fabregas.
"The team, the club, the fans have all grown. It's incredible. We will remember this day 20 years from now."
Como are sixth and just two points behind fourth-placed AC Milan who host Atalanta in the day's late match at the San Siro.
Milan are level on points with fifth-placed Roma, who are still in the hunt thanks to late penalty drama at Parma.
Gian Piero Gasperini's side looked to have thrown away their chances of a top four finish when Mandela Keita shot Parma ahead with three minutes remaining.
But Devyne Rensch shot the away side level in the third minute of stoppage time and moments later was brought down by Sascha Britschgi.
From there chaos ensured as referee Daniele Chiffi initially thought Rensch had fouled Britschgi in a penalty area tussle.
But Chiffi was called to the pitch-side monitor by the VAR and gave a spot-kick which Donyell Malen, who had put Roma ahead in the 22nd minute, smashed home his 14th goal of the season to the delight of the away fans.
Roma haven't played in Europe's top club competition since being knocked out by Porto in the last 16 seven years ago, and have the small matter of the Rome derby next weekend.