The 19-year-old linked up for both of his goals with Mathys Tel, poking home the French forward's ball from the left after a well-judged run in the 59th minute at the Tottenham Hotspur Stadium.
He then shot into the bottom corner after further fine work from Tel down the left 20 minutes later.
Richarlison had given Spurs the lead in the 35th minute, finishing with his left foot after a ball across the area from Andy Robertson, a recent signing from Premier League rivals Liverpool.
Moore spent last season on loan at Scottish giants Rangers and has been linked with another loan move for the new campaign, last featuring in competitive action for Spurs in May 2025.
Spurs will finish their pre-season campaign with a second match against German side Hoffenheim at their London training ground on Sunday.
Tottenham's Premier League campaign begins on 22 August away to fellow London club Brentford.
Roberto De Zerbi's side are unbeaten in pre-season, winning five -- including a penalty shootout victory -- and drawing one of their six matches.
England full-back Djed Spence was not involved on Saturday as he completed a move to Inter Milan.
