The Wales international has enjoyed a resurgence in the last few weeks after a miserable start to his Spurs homecoming and delivered his most telling impact yet against the Clarets.
He then added a brilliant second after the break to complete a fine afternoon's work to help Spurs to just a second Premier League win in seven games.
It may have taken the 31-year-old the best part of five months to find his groove but he could not have timed it better as Spurs head into a crucial part of the season, with the latter stages of the Europa League and a Carabao Cup final to look forward to.
Burnley will not be too fussed about returning to the Tottenham Hotspur Stadium any time soon as they followed last season's 5-0 thumping here with another heavy defeat that could have been even worse but for goalkeeper Nick Pope.
Bale needed just 67 seconds to make an impact as Spurs made a dream start.
Son Heung-min received the ball on the left and his low cross was poked home by Bale, whose late run beat the offside trap.
It was an electric beginning by Spurs, who could have been out of sight in the opening 10 minutes but Kane fizzed an effort inches wide and then Moura fired straight at Pope.
Bale then rolled back the years to cruise past Charlie Taylor before combining with Kane and Son but the counter-attack broke down at the last moment.
Bale was everywhere and notched a brilliant assist in the 15th minute when he set Kane clear with a 50-yard pass. The England captain still had work to do and he fired in his 14th league goal of the season, though was grateful for a deflection off James Tarkowski that took it past Pope.
The Real Madrid loanee could have had another goal soon after as another quick break saw him played in by Son, but he fired over after cutting inside on to his left foot.
Instead he had to settle for a pre-assist as Spurs made it 3-0 in the 33rd minute.
His ball found Sergio Reguilon in space and the Spaniard's cross fell to Moura who fired into the corner for his second league goal in two games.
Spurs had been 3-0 up at half-time against West Ham in October and went on to draw 3-3 but they made sure there was to be no repeat as Bale got his second of the game 10 minutes after the restart.
Son again made it as he created space on the left before advancing and switching play to Bale, who, with an air of inevitability, cut inside and fired into the bottom corner.
Spurs could have racked up their record win at their new home had they remained as clinical in the final 30 minutes.
After Bale had departed for a well-earned rest, Kane forced Pope into a brilliant flying save with a swerving shot from distance before the England goalkeeper did even better shortly after.
A devastating counter involving Kane and Dele Alli ended with Son in on goal, but his low shot was superbly kept out.
Son blazed another late chance over and Kane also fluffed his lines but the damage was done as Spurs stopped the rot.