Portugal s forward Cristiano Ronaldo celebrates after scoring his team s first goal during the UEFA Euro 2024 group J qualification football match between Luxembourg and Portugal at the Stade de Luxembourg, in Luxembourg, on March 26, 2023. AFP
Captain Kane, who broke Wayne Rooney's all-time England goalscoring record in midweek, turned home his 55th international goal from Bukayo Saka's cross in the 37th minute.
In-form Arsenal winger Saka all but ended Ukraine's resistance three minutes later, turning from Jordan Henderson's pass and curling a sublime strike from outside the area into the top corner.
The victory takes England three points clear at the top of the early Group C table after winning in Italy for the first time since 1961 on Thursday.
"Two wins out of two is all we asked for at the start of the camp," midfielder Jude Bellingham told Channel 4.
"We've followed up a really good result in Italy with another one tonight and when you do that, it feels rewarding."
Gareth Southgate's men produced an accomplished performance in their first home game since an agonising World Cup quarter-final defeat by France last December.
Kane missed one great early chance before he gave England the lead.
Ukraine failed to muster a shot on target and Conor Gallagher, Harry Maguire and Jack Grealish all went close to netting a third for the hosts late on.
England, still waiting for a first major tournament title since 1966, return to qualifying action against Malta and North Macedonia in June.
The top two teams in each group will automatically book a place in next year's European Championship in Germany.
Reigning champions Italy bounced back from their loss to England with a straightforward 2-0 away win over Malta.
Argentine-born forward Mateo Retegui followed up his debut goal against England by opening the scoring early on.
Monza midfielder Matteo Pessina made it two before the half-hour mark and Italy comfortably saw out the victory.
Ronaldo scores twice
Ronaldo marked his record-breaking 197th international appearance in midweek with two goals against Liechtenstein and he repeated the trick as Portugal thumped Luxembourg 6-0.
The 38-year-old diverted in Nuno Mendes' headed pass to give Roberto Martinez's men a ninth-minute lead.
Goals from Joao Felix and Bernardo Silva put the game to bed inside 18 minutes, before Ronaldo slotted home his second from Bruno Fernandes' through ball in the 31st minute.
Ronaldo has now scored 11 goals against Luxembourg in his career.
Late strikes from substitutes Otavio and Rafael Leao, who also missed a penalty, rounded off a fine performance from Portugal who are already clear at the top of Group J.
Elsewhere in the group, Iceland bounced back from their opening defeat by Bosnia and Herzegovina by thrashing Liechtenstein 7-0.
Slovakia moved into second place behind Portugal with a 2-0 win over the Bosnians.
Denmark blew a two-goal lead to crash to a surprise 3-2 defeat in Kazakhstan.
The Euro 2020 semi-finalists appeared to be cruising to victory in the Group H match as Atalanta youngster Rasmus Hojlund netted twice in the first half after scoring a hat-trick against Finland on Thursday.
Kazakhstan had started their bid to qualify for a first ever major tournament with a home defeat by Slovenia.
But Bakhtiyor Zaynutdinov's 73rd-minute penalty gave the hosts hope of a famous turnaround in Astana.
Midfielder Askhat Tagybergen crashed a long-range drive past a helpless Kasper Schmeichel with four minutes of normal time remaining to equalise.
Substitute Abat Aymbetov provided the golden moment for Kazakhstan -- who have already at least secured a Euro 2024 play-off spot through the Nations League -- leaping to power a header into the top corner in the 89th minute.
He was later sent off for a second yellow card but by then had already grabbed all three points.
Slovenia battled to a 2-0 victory over San Marino in the second Group H match to move top of the early standings.
Finland edged out Northern Ireland 1-0 in Belfast to make it four teams with one win behind Slovenia.
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