The 19-year-old's second-half goals were both set up by Mathys Tel after Richarlison hit a first-half opener from Andy Robertson's cross.
Four new summer signings - Robertson, Sandro Tonali, Jan Paul van Hecke and Marcos Sensi - all made their home debuts in the win, which keeps Spurs unbeaten in pre-season.
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But there were some notable absentees from the victory, including Micky van de Ven, James Maddison and Mateus Fernandes.
Spurs fans will be hoping some of the missing players will play a part in Sunday's final pre-season game against the same opponents in a behind-closed-doors game at the club's training ground.
Roberto De Zerbi's side then open their Premier League campaign at Brentford next Saturday, live on Sky Sports.
Here, Sky Sports assesses Spurs' pre-season win over Hoffenheim in their first home game since avoiding relegation in May…
Moore and Bergvall shine amid uncertain futures
Two players who were linked with moves away from Spurs delivered good performances in the win.
Moore was on the cusp of a loan move to Bundesliga side Cologne last week, but with that now on hold the teenager has given De Zerbi plenty to ponder with his two-goal display.
The 19-year-old produced a muted celebration for his first, as he tapped in Tel's cross, but he showed his delight for his second as he deftly finished off Tel's pass.
The Spurs academy graduate's destination for the new season is still undecided.
Meanwhile, Lucas Bergvall looked like he might be leaving Tottenham two months ago.
Newcastle and Nottingham Forest were interested in the midfielder, and it remains to be seen whether he will be at the club after deadline day.
De Zerbi insists he wants to keep the midfielder after addressing the player's concerns over lack of game time
The Sweden international has been playing regularly in pre-season, and his display at the Tottenham Hotspur Stadium on Saturday would have encouraged his head coach.
Michael Bridge
Robertson impresses with fine assist
Andy Robertson left Liverpool because he wanted more game time - and on this evidence he will be getting it.
The Scotland international was superb on Spurs' left side in the win as he delivered cross after cross, with a pinpoint delivery for Richarlison's opener.
The 32-year-old's arrival was seen as a great move for the Spurs dressing room, as he brought a wealth of winning experience, but against Hoffenheim he showed his on-field quality.
With fellow left-back Destiny Udogie still yet to play in pre-season and concerns around the Italy international's fitness, Robertson has taken advantage of his absence.
The ex-Liverpool defender looks nailed on to start at Brentford next Saturday for Spurs' Premier League opener - and on this form, Udogie could well find it tough to oust the man eight years his senior.
Declan Olley
Kinsky proves his No 1 status
Spurs' clean sheet in the win was largely thanks to Antonin Kinsky.
The Tottenham goalkeeper made several saves to keep Hoffenheim at bay, thus proving his new number one status.
Kinsky also dealt adeptly with crosses and was good with the ball at his feet, showing why he will be a great fit for De Zerbi's system.
It is some turnaround for the 23-year-old since his horror show in Madrid seven months ago, and he has deservedly taken the spot of Guglielmo Vicario, who was not involved on Saturday with Juventus eyeing a move for the Italy international.
Declan Olley
