Wilfried Zaha put the Eagles ahead early on and the hosts appeared in control but the Saints skipper was on hand to turn the game on its head with a superb 32nd-minute equaliser.
Ward-Prowse curled his effort over the wall and into the top corner from 25 yards to score directly from a free-kick for the 11th time in the Premier League, putting him joint-third on the all-time list.
It sparked the visitors into life at Selhurst Park and Armando Broja drilled them ahead minutes later, but they had to settle for a point after Jordan Ayew levelled for Palace midway through the second half.
Hasenhuttl said of the free-kick: “It helps massively because it was suddenly very calm in the ground here and our fans woke up.
“This is what you need in that moment. It was fantastic how our fans were fighting with us and supporting us until the end. It is always a pleasure to have them with us and to give everything we can give them.
“For Prowsey, it was a good moment to show his quality and then the belief was there to play how we wanted to play.
“We had massive opportunities to score more and, yeah, second half I saw a game from both teams fighting for everything.”
Despite a point in London, Southampton remain six games without a win and Hasenhuttl admitted they need to try to earn more free-kicks in central areas to help their captain exploit his talent even more.
“It is such a good weapon we have to be more often in a situation where the opposition can foul us,” the Austrian stated.
“I am very happy to have him in my squad and I am very happy he has this quality. We must give him more free-kicks in this position, I think.”
Palace boss Patrick Vieira conceded watching Ward-Prowse find the net from a free-kick was “painful” but acknowledged the England midfielder possesses the ability to cause problems.
He added: “It is painful but you have to recognise the quality of the player on set-pieces.
“When it is a corner or right free-kick, or central free-kick, we knew that it is one of the strengths of their team. He took his chance really well and in that situation you just have to congratulate the player.”
Vieira was less impressed with his team’s overall display and insisted they did not deserve to win.
“When you look at the game overall, I am pleased to take a point because I think they played some really good football, they pressured us quite high and we didn’t manage to play through that pressure,” he said.
“At the end they had a couple of chances and situations as well, so I think the point we took tonight, regarding the way we played, I don’t think we deserved more that.”