First-half goals from Kane and Lucas then compounded Burnley’s problems as they went in three goals down at half-time.
A quieter second-half performance saw Bale grab his second goal to complete a dominant showing from the hosts, who end up with 4-0 victors over the Clarets.
Tottenham’s win lifts them to eighth in the table, back up above Aston Villa and London rivals Arsenal.
The next fixture for Mourinho’s side sees them make the short trip to Fulham, while Burnley, who were fairly poor in this game, remain 15th and they next host Leicester City.
After being granted a rare starting opportunity, Bale repaid Mourinho’s faith by opening the scoring after 68 seconds.
The opening goal, scored inside two minutes, carried a whiff of fortune, given Son Heung-Min appeared to be targeting a deeper cross to Harry Kane rather than the low cutter into space between James Tarkowski and Nick Pope. In truth, it looked like he scuffed it.
From there, Bale read the path of delivery, opened his body and side-footed past Pope.
Kane and Moura both came close ahead of the second goal, and Bale’s wider contribution included the destruction of Charlie Taylor.
He played the ball down the line and then hammered the left-back for pace – just like the olden days. His subsequent retrieval of possession near Tottenham’s area earned equal applause from Mourinho before Bale pinged the 60-yard ball that made the goal for Kane.
Kane’s shot to the near post deflected off Tarkowski and its trajectory was raised sufficiently to clear Pope’s upper hand.
Dyche looked pretty peeved and his side soundly beaten, and not even 16 minutes had been played.
Bale’s finest moment in a good bunch came 10 minutes into the second half. Son led the break – yet another break in a game of many – and crossed the field with his left-to-right pass to Bale, who had been allowed a ludicrous amount of space.
He had a touch to set himself on the edge of the area and curled a shot in off the post with his left.
Mourinho brought on Dele Alli for Moura for the final 25 minutes, and rather like Bale, the Englishman also appears to be on an upturn.
After a strong Europa League showing in midweek, he was denied a start here but showed verve in his limited window of time, most clearly in a through ball for Son that almost led to a fifth goal.
Bale was soon replaced for Erik Lamela, having more than excelled in only his third start of the season.
His home start for the Spurs in the league was in 2013 – he scored that day against Sunderland as well. Rather a lot has happened in the meantime, but at least he is looking more like his old self.