Bruce had seen his side slip to a 1-0 home defeat to Arsenal and a tame 3-1 loss to Norwich City in his opening two matches since taking charge.
Those setbacks only served to deepen the gloom that followed Rafael Benitez's departure, but Newcastle produced a superb away performance as Spurs suffered an early slip up in the 2019-2020 season.
Tottenham was behind for much of its opening 3-1 win over Aston Villa but was unable to produce a similar turnaround this time, though the host side was controversially denied a penalty after Jamaal Lascelles appeared to impede Harry Kane.
Newcastle was dealt an early blow when Allan Saint-Maximin limped off with a hamstring injury while wastefully running the ball out of play in a free-kick routine.
The visitor was then fortunate not to concede a penalty when Fabian Schar appeared to bring down the returning Son Heung-min.
However, Tottenham's defence failed to heed the warning of Sean Longstaff forcing Hugo Lloris to tip over, allowing Joelinton too much space to collect a Christian Atsu cross as Newcastle's record signing confidently fired in from close range.
Son stung the palms of Martin Dubravka with a half-volley and then dragged another effort wide before Lucas Moura miskicked a chance to equalise with the goal at his mercy.
A last-ditch tackle from Schar prevented Erik Lamela from levelling from Son's deflected effort and Spurs were apoplectic when Lascelles fell to the ground and took Kane with him, only for referee Mike Dean to reject shouts for a penalty and have VAR back him up.
Lucas and Kane both spurned glorious late opportunities for Tottenham as Newcastle held on for a result that should serve as a much-needed morale boost.