The defeat means Wolves remain in 12th place and means they will finish in the bottom half of the table for the first time since they gained promotion back to the top-flight in 2018.
The game started brightly and Kane's long-range effort came off the post after six minutes.
Spurs had the better chances in the first half and went close to scoring after 44 minutes but Wolves defender Conor Coady produced two stunning goalline clearances from a corner.
Moments later, Spurs went ahead after Kane beat the offside trap and slotted the ball past goalkeeper Rui Patricio.
The Spurs captain is now the fourth player to have more than 35 goal involvements in two different Premier League seasons (2016-17 and 2020-21), after Thierry Henry (four), Alan Shearer (three) and Robin van Persie.
The hosts almost doubled their lead 10 minutes after the break but Kane's effort was tipped onto the post while Dele Alli followed up to also hit the woodwork.
Spurs grabbed a second just after the hour mark when Hojbjerg was the quickest to react to score a tap in after Patricio blocked Gareth Bale's strike.
"We are not happy with where we are, we should be higher and we only have ourselves to blame," Alli, who fell out of favour under previous manager Jose Mourinho, told Sky Sports.
"We are showing now what we can do but it is a bit too late. We just have to keep working hard and take it into the next season as well."
Although Spurs would need a sensational set of results to finish in the top four and qualify for the Champions League, sixth place should be enough to make the Europa League next season following Leicester City's FA Cup win on Saturday.