The 31-year-old, England's all-time leading goalscorer, was honored with a golden cap prior to kickoff to celebrate becoming just the 10th male English player to reach a century of caps for his country.
Kane and co were initially left frustrated by the low block of Finland, who defended resolutely in the first 45 minutes and in the early stages of the second half, but England's No.9 made his presence felt shortly before the hour mark.
Indeed, just moments after trying his luck with a overhead kick, which was well saved by Finland's Lukas Hradecky, Kane fired England in front in the 57th minute with a thunderous right-footed shot that pinged off the underside of the crossbar and over the line.
Fourteen minutes from time, Kane doubled his tally and scored his record-extending 68th England goal with a sweet first-time strike following a neat one-two between Trent Alexander-Arnold and Noni Madueke - one of two debutants at Wembley along with Lille's Angel Gomes who was handed his first start by interim boss Lee Carsley.
England eventually cruised to their second successive Nations League victory, three days on from beating the Republic of Ireland 2-0 in Dublin, and they now sit level on points with League B Group A leaders Greece, who beat Ireland 2-0 on home soil.
ENGLAND VS. FINLAND HIGHLIGHTS
Harry Kane vs. Finland (57th min, England 1-0 Finland)
It just had to be him! Kane had his fair share of chances in the final third to mark his special night with a goal, but he had to wait until the 57th minute to eventually make the net ripple and open the scoring for England.
Just moments after Hradecky made two great saves to deny Anthony Gordon and an overhead kick from Kane, the Finnish goalkeeper could not stop a thunderbolt from England's No.9 inside the penalty area.
Kane, wearing golden boots on his golden occasion, received the ball on the half-turn and shifted it on to his right foot before unleashing a superb strike which flew past Hradecky in off the underside of the crossbar.
Harry Kane vs. Finland (76th min, England 2-0 Finland)
Chelsea's Noni Madueke was brought on for his senior England debut midway through the second half, and the winger made a notable impression on the right flank as well as provided the assist for Kane's second goal.
Madueke linked up well with Alexander-Arnold down the right, receiving a smart first-time through-ball from the Liverpool right-back before flicking the ball into the path of Kane, who whipped a sweet right-footed strike beyond Hradecky.
MAN OF THE MATCH - TRENT ALEXANDER-ARNOLD
While Kane will understandably be in the headlines for his brilliant brace on a landmark occasion, Trent Alexander-Arnold was a standout performer for England and deserves all the plaudits that come his way.
The Liverpool right-back created a total of six chances and produced 18 passes into the final third against Finland, more than any other player on the Wembley turf, while he was also involved in both goals, setting up Kane's first with a driven pass before sending Madueke through down the right to assist Kane for his second.
A special mention should also go to 24-year-old Gomes, who impressed in midfield both in and out of possession on his debut.
ENGLAND VS. FINLAND MATCH STATS
Possession: England 79%-21% Finland
Shots: England 22-2 Finland
Shots on target: England 8-0 Finland
Corners: England 8-2 Finland
Fouls: England 6-8 Finland
BEST STATS
WHAT NEXT?
Both England and Finland are next in Nations League action in October, with the Three Lions travelling to Helsinki for the reverse fixture against Finland on October 10, before facing Greece at Wembley three days later.
Meanwhile, Finland play host to the Republic of Ireland at the Helsinki Olympic Stadium on October 10, before welcoming England to the same venue three days later.