The match was played in a fantastic atmosphere with Welsh fans drowning out Al Rayyan but meeting their match in the typically vocal US supporters, whose drums barely stopped beating.
A lively opening 15 minutes saw the US nearly open the scoring from a Wales own goal and a Josh Sargent header seconds apart, while both Sergino Dest and Weston McKennie were handed yellow cards for hard fouls.
Gregg Berhalter's side continued to look the more dangerous of the two and opened the scoring late in the first half when Weah cleverly finished off his chance from a quick-hitting counterattack after being played in behind the defense by Christian Pulisic.
It was a tale of two halves and Wales manager Rob Page made the key change at half-time when he replaced the ineffective Dan James with the taller Kieffer Moore, who was exactly what the side had been missing in the opening period.
"It felt like in the first half we had a lot of energy, a lot of momentum," Weah said after the match. "And then coming into the second half we dialed down and Wales turned it up a notch. They started pressing us, they had most of the ball and I think at the end that's what really hurt us."
With the US headed for a massive win to begin the World Cup, Bale drew a foul from Walker Zimmerman in the penalty area and delivered an unstoppable spot kick to beat Turner to level the game for good despite 10 minutes of second-half stoppage time.
"To go a goal behind against a good team like the US, we showed character, credit to the lads for coming back and getting a point," Page said. "When we got the penalty we knew who was taking it, one million percent.
"He's never let us down has he? It's all about Bale and rightly so."
On the US side, Zimmerman acknowledged his mistake in fouling Bale, but credited Wales' all-time leading scorer for a professional move to put himself in the position in the first place.
"He probably just puts his leg not for the ball but to try and get in the way of me hitting the ball," Zimmerman said. "So I kind of went through him and I think I still got the ball. But clever move -- I wish I would have seen him out of the corner my eye."
The US finished with four yellow cards, the team's most in a World Cup match since drawing five against Germany in 2002, while Wales were twice cautioned in the game.
"Wales were very direct in the second half," Berhalter said. "They have a big team and they made it very difficult. They stepped up the pressure.
"But I thought the guys handled it well. We kept it up to the end, it was a hard-fought game and we left everything out there."
Looking ahead to the rest of the group stage, Weah added: "In a World Cup, the most important thing is that we didn't lose. We need to continue to do what we do best and keep working."
Information from Reuters was used in this report.