Wotherspoon created the only goal of the game for Saints midway through the first half with a brilliant run and pass which May tucked away for his 20th goal of the season.
It was just Saints' second away victory of the season in the league and the result means Thistle are still winless at home.
May's goalscoring exploits has been grabbing the headlines this season but Wright confirmed he wanted to sign striker Goodwillie to help him out, only to be thwarted by the asking price.
"That's dead in the water for us," he said. "We won't be able to match what Blackburn are looking for in terms of doing a deal. So we'll have to move elsewhere. I do feel I need a striker in and we may look at the midfield area as well."
Wright insists Wothrrspoon is equally worthy of praise as May.
He said: "David Wotherspoon has been a dream for us this season as he can play in so many positions - either on the right, in off the left or behind the striker.
"He had a shot by drifting off the left just before he created our goal that was close. I'm really pleased with him and it was a great assist for Stevie, who tucked it away nicely.
"I'm pleased with our night's work. The players showed great character, especially after a difficult game on Saturday.
"To come here and start so well is pleasing. But we have managed that in the last three games. We dominated early on and created a few chances and when we scored we were more than deserving to be 1-0 ahead.
"It was after we scored our goal that we started to make wrong decisions. We started to give the ball away far too cheaply and gave Partick far too much possession. They are a good side with good players, but, other than a few shots from distance, I don't think our keeper Stevie Banks had too much to do."
Partick boss Alan Archibald admitted the visitors were well worth their half-time lead but felt his team's second-half exertions were worthy of a point.
He said: "We were lucky to go in at half-time only 1-0 down. They were the far better side - they dominated all over the pitch for about 35 minutes.
"With 10 minutes to go in the first half we got a wee bit of life about us which we took into the second half and were a lot better. We could have got a point.
"But the first half was as poor as we've played in the league. Even in the second half, we gave the ball away in silly areas. I don't think the start was down to the results at home as we've been good in the past two games."