Switzerland forward Noah Okafor scored his first international goal as the Swiss beat Bulgaria 4-0 to win Group C and send Italy back to the play-offs for next year's World Cup in Qatar.
Ruben Vargas, Cedric Itten, and Remo Freuler scored for the hosts, who now have 18 points from eight games, two more than the European champions.
Italy and Switzerland both had 15 points in Group C going into the final qualifiers, but the Azzurri had a better goal difference, which would be the first tiebreaker if they finished level on points.
However, the Italians were halted to a 0-0 draw away to Northern Ireland and will now have to compete in the play-offs in March.
In their match against San Marino, England scored four goals in a 10-0 thrashing, confirming Gareth Southgate's side's spot in the finals.
In reality, England just needed a point against the 210th and lowest-ranked soccer nation in the world to secure top spot in Group I, thus the only question was how many goals they would score to commemorate the event.
Kane dutifully filled his boots, following up his hat-trick in England's 5-0 win over Albania with four goals before half-time, including two penalties, to take his England tally to 48 and tie Gary Lineker for third all-time.
After a sixth-minute header from Harry Maguire and an own goal from Filippo Fabbri, Kane took over and put England 6-0 up at half-time.
Emile Smith Rowe scored his first England goal making it seven, and San Marino's punishment worsened after Dante Rossi was sent off in the 68th minute for a second yellow card.
Tyrone Mings, Tammy Abraham, and Bukayo Saka all scored in a farcically one-sided contest that did little to improve international soccer's standing.
Scotland, along with Portugal, Italy, and Russia, is one of four teams guaranteed to be seeded — and hence play at home – in the play-off semi-finals.
- Northern Ireland 0-0 Italy
- Switzerland 4-0 Bulgaria
- Austria 4-1 Moldova
- Israel 3-2 Faroe Islands
- Scotland 2-0 Denmark
- Albania 1-0 Andorra
- Poland 1-2 Hungary
- San Marino 0-10 England
Who has qualified so far?