As a bonus the winning goal was scored by 20-year-old James McPake, one of the three promising youngsters promoted to the first team last weekend.
Out of favour skipper Stuart Lovell, who still faces the sack after criticising the club in the papers, came on as a substitute for the last six minutes to suggest that he may have a future under Gough's new regime.
Moments after his triumphant arrival in the home dugout, Gough must have been horrified as one of the finest defenders of his generation watched his new team make a real hash of things at the back.
Fortunately for Livingstone goalkeeper Roddy McKenzie was alert to the danger and rushed out to smother a close range shot from Bobby Mann.
An early injury to Iain Anderson prevented Dundee from continuing the momentum of their lively start, although Livingstone struggled themselves as Oscar Ramos Rubio headed well over and Jim Hamilton sliced a shot towards the corner flag.
It all left Gough scratching his head in bemusement and it might have got a lot worse in the 20th minute when Dundee's top scorer Steve Lovell somehow lost his balance with only McKenzie to beat after John Sutton's long ball had beat the Livi defence.
Sutton himself then missed a free header, but just as Livingstone looked to be rocking they took the lead with a stunningly simple goal. Jason Dair hacked the ball clear from his own penalty area and Hamilton nodded it into the path of McPake, who left Mann for dead before side-footing past keeper Derek Soutar.
McPake and Hamilton combined again in the 33rd minute with Hamilton firing a first time shot inches over the bar after McPake's pace had unsettled the Dundee defence. Shortly before half-time, Hamilton had a header saved by Soutar.
Sutton wasted a perfect opportunity to equalise early in the second period following terrific wing play from Lovell when he slid the ball straight into McKenzie's hands as the keeper scrambled across his line.
Derek Lilley then blew a great chance to kill Dundee off as he missed the ball completely 18 yards out.
In all, we played well enough to get 3 points, Dundee were unlucky not to get anything from the match, but great saves by Roddy McKenzie kept the Dark Blues out.