The Welsh looked destined for defeat in their first appearance in the tournament for 64 years after Timothy Weah opened the scoring in the first half.
The breakthrough came on 36 minutes as Christian Pulisic found space to slip a pass in behind for Weah, who smartly jabbed the ball past Hennessey and into the bottom corner.
Wales had been overwhelmed in the first half and in response manager Rob Page brought on Kieffer Moore for the ineffective Dan James at the break.
And the Bournemouth striker should have levelled for Wales on 65 minutes, as he rose at the near post from a corner, but somehow headed over with the net at his mercy.
With eight minutes to go they did find the equaliser, however. Bale got himself in front of Walker Zimmerman in the box to be tripped and win a penalty, before stepping up himself to thunder the ball past Matt Turner.
“He’s never let us down,” Wales manager Rob Page told ITV. “Once again it’s all about Bale and rightly so.”
He always makes a difference for his country. It had, in truth, been a quiet performance from Bale up until he provided the decisive moment late in the second half.
The 41st goal for his country, a first for Wales in the World Cup for 64 years. It was always going to be him to make the difference.
“We’ve been talking about Bale all day and it’s always about moments for this player,” Roy Keane told ITV.
“It’s written in the stars for him when he turns out for Wales, and it was a great finish.”
He has been the leader of his country for so long, but he doesn’t seem to feel the pressure or the burden of responsibility. In fact, he relishes it.
“There were no doubts in my head [I was going to take the penalty},” Bale told ITV. “I have to step up and I’m happy to do so.”
The result leaves both sides trailing England in Group B, after they earned all three points against Iran on Monday afternoon.