Saints won 3-2 as Ward-Prowse set up Jack Stephens for Southampton's second goal, before scoring the third from a free-kick.
"No matter how we won the game, it's just important that we dug in deep. Ok, we've not been playing the best of football, but we dug in together and got the vital three points."
Ward-Prowse had to fight off Sofiane Boufal's desire to take what proved to be the decisive free-kick, but he said that moment simply showcased the desire that exists within the whole team to get out of trouble in the table.
"There's a bit of competition for the free-kicks, but it shows how passionate we all are," he said.
"There's a good feeling around the team and all the lads want to do well to help the team. Thankfully for me, I was able to do that today, but Sofiane played brilliantly and did his part as well."