Stephan El Shaarawy ended a three-year drought by scoring the winning goal as Italy beat Azerbaijan 3-1 Saturday to qualify for next year's European Championship.
After Eder's opener and an equalizer from Dmitri Nazarov, El Shaarawy finished off a counterattack in the 43rd for his first national team goal since November 2012.
Manchester United's Matteo Darmian added another for Italy in the second half in Baku.
"Now that we've qualified it might have seemed easy but there's nothing easy," said Italy coach Antonio Conte, who took over when Cesare Prandelli resigned after the Azzurri's first-round elimination from last year's World Cup.
"We're improving," Conte added. "Now we've got to continue like this, recuperate and honor the qualification by going to Rome and playing a good match against Norway."
Norway took a big step toward qualifying for the tournament in France with a 2-0 win over Malta.
Alexander Tettey and Alexander Soderlund scored either side of halftime for Norway in Oslo.
Norway is seeking its second tournament appearance after exiting from the group stage in 2000.
Italy has 21 points in Group H, Norway is next with 19 and Croatia is third with 17. Bulgaria was eliminated with eight points, Azerbaijan has six and Malta two.
Croatia beat Bulgaria 3-0 with goals from Ivan Perisic, Ivan Rakitic and Nikola Kalinic. The match was played in an empty stadium in Zagreb as part of the punishment for a swastika that was painted on the pitch before a match against Italy in June.
Croatia was also deducted a point for the swastika incident.
Croatia's Duje Cop was shown a red card in the final minutes for a hard tackle.
The top two finishers from the nine groups qualify automatically. The best third-place finisher also qualifies automatically, while the eight other third-place teams can reach the tournament through a playoff.
Norway is guaranteed at least a playoff spot, although Croatia holds the tiebreaker with a better head-to-head record.
Italy can secure first place against Norway in Rome on Tuesday, while Croatia visits Malta.
Still, winning the group might not be enough for Italy to get a top seed in the Euro 2016 draw.
"Croatia is ahead of us in the FIFA rankings but we're ahead in the UEFA rankings," Conte said. "These are mechanisms that I have a hard time understanding."
The Azzurri are under pressure to perform after getting eliminated from the group stage at the last two World Cups. Since winning the 2006 World Cup, Italy's only highlight was reaching the final of Euro 2012.
On a rainy evening in Baku, Azerbaijan played its first match in the new Olimpiya stadium, while Italy had to overcome the absence of injured playmaker Andrea Pirlo.
Eleven minutes in, Pirlo's replacement Marco Verratti launched a long, vertical pass for Eder that gave the Brazilian-born forward plenty of room to glide past the defense and easily beat goalkeeper Kamran Agayev.
It was Eder's second goal in five matches for Italy. He also has six goals in seven Serie A matches this season for Sampdoria.
Minutes later, Eder turned provider for Graziano Pelle, who shot on target and had Agayev tip his effort over the bar.
Just after the half-hour mark, a defensive lapse allowed Nazarov to score from the edge of the area, with Giorgio Chiellini and Leonardo Bonucci sharing the blame.
El Shaarawy restored Italy's lead by redirecting a cross from Antonio Candreva into an empty net on a play that began with Pelle.
The son of an Egyptian father and an Italian mother, the 22-year-old El Shaarawy has been hailed as one of Italy's best young players for years but he struggled with injuries and confidence in recent seasons. After failing to make Italy's squad for last year's World Cup, El Shaarawy transferred from AC Milan to Monaco.
In the 61st, a lob effort from an outstanding Eder was cleared off the line by Azerbaijan captain Rashad Sadygov, who was celebrating his 100th national team appearance.
Four minutes later, Darmian got his first goal for Italy with a long, powerful effort after taking a loose ball beyond the area.
Azerbaijan defender Badavi Huseynov was shown a direct red card for a last-man foul on substitute Sebastian Giovinco in the 88th and Giovinco's ensuing free kick hit the crossbar.