Bale scored the first, a rare header, in the fifth minute to take his tally to 11 goals in his last nine games and he set up Jan Vertonghen for the hosts' third after Sigurdsson had scored the second.
The Welshman, who famously came of age when he scored a hat-trick against Inter in the Champions League in 2010, was thrilled Spurs were able to thoroughly dominate the Italian giants.
"We played well and set the tempo from first whistle," he told ITV.
"We immediately made it difficult for them, it was a great performance and a worthy result to be honest.
"It's always nice to get a goal however it comes and I'm enjoying playing. It was a great performance and we take a great lead into the away leg with no away goals for them."
The only downside for Bale is that he will miss the chance to remind Inter of his qualities in the second leg next week due to suspension after being booked, not for the first time this season, for diving when he went down in the Inter box
However, striker Jermain Defoe thinks Tottenham will be able to cope without the destructive winger.
"Hopefully we've done enough but it's always going to be difficult going there with their home fans and they're still a top side," he said.
"It's going to be difficult but saying that I think with the we played tonight if we do that over there then we shouldn't have any problems."
England striker Defoe started his first game in over a month and was delighted to play a part in a memorable night at White Hart Lane.
"It's always nice to get back playing after an injury, I felt strong," he added.
"In the squad and a good result so I'm delighted."
Spurs boss Andre Villas-Boas was equally ecstatic with the result but was quick to sound a note of caution.
"It was a full 90 minute performance and excellent attacking football," he said.
"We tried to reduce their chances to the limit and had so many opportunities.
"It was a great game and a great European night but unfortunately we aren't through yet, we have to go there and it is a difficult place to go."