Italy applied the pressure on England ahead of their match with the Group C leaders by cruising to a 4-0 victory over Malta on Saturday, while Denmark, Slovenia and Hungary all won to close in on qualifying for Euro 2024.
European champions Italy, who failed to qualify for the 2022 World Cup in Qatar, had few problems at the Stadio San Nicola in Bari against a struggling Malta side without a win so far in the qualifying campaign for the tournament in Germany.
Luciano Spalletti's side were missing several key players, including Ciro Immobile, Lorenzo Pellegrini, Mateo Retegui and Federico Chiesa, all sidelined by injury.
Sandro Tonali and Nicolo Zaniolo also left the squad earlier this week after being informed of their involvement in an investigation by Turin prosecutors.
Italy's win leaves them in second place ahead of Ukraine on the basis of head-to-head record; Italy defeated Ukraine 2-1 in Milan last month, with the reverse fixture in Germany set for November 20.
Ukraine stayed level with Italy on 10 points following a 2-0 against North Macedonia, although the Azzurri have a match in hand on all their group rivals except England, who top the group with 13 points.
England host Italy in their next qualifier on Tuesday.
Giacomo Bonaventura opened the scoring after 23 minutes, netting his first international goal with a skillful curled effort into the top corner from just inside the penalty area.
At 34 years and 53 days, midfielder Bonaventura became the oldest Italy player to score his first goal for the national team – more than 10 years after his debut.
"Sorry it took so long, I got there eventually," he told Sky Sports Italia. "I was lucky, it went well ... these games against a very defensive team are tough to open the scoring."
Domenico Berardi increased Italy's lead with a left-foot curler just before halftime and added his second goal in the 64th minute with a precise finish from a cut-back.
In the closing moments, Davide Frattesi scored the final goal of the night, slotting a low shot from the edge of the area into the bottom corner.
Spalletti praised his side for their determined approach to the match against the group minnows.
"The important thing is the three points, never letting it be in doubt, without taking this test lightly, showing a professional attitude," Spalletti told RAI Sport.
"You can see these players are eager to get to know each other more and play good football, so we are pretty pleased."
Italy face England at Wembley Stadium on Tuesday when a win would put them level on points with Gareth Southgate's side, who will themselves clinch a place at the finals with a victory.
"That is a match where we can really see what our potential is. Once we have played, then I'll tell you what that potential is," added Spalletti.
Hungary stay top of Group G
Hungary remain top of Group G after beating second-placed Serbia 2-1, with all the goals coming in the first half. Hungary have 13 points, three points above Serbia with a game in hand.
The Hungarians will qualify for the European Championship if they win away to Lithuania on Tuesday.
In Group H, leaders Slovenia beat third-placed Finland 3-0 with a Benjamin Sesko double, including a penalty and a late goal by Erik Janza. They are level on 16 points with second-placed Denmark, who won 3-1 at home to Kazakhstan.