Cobblers striker Emile Sinclair fired the visitors ahead with a clinical finish following a lightning 10th minute counter attack.
Sinclair doubled Town's tally six minutes later with an even better finish from an acute angle as United's defence was again found wanting.
Torquay centre-back Krystian Pearce gave United some hope with a 45th minute side-foot volley finish to steer in substitute Jordan Chapell's corner but it was just a consolation and the Cobblers were able to close the gap to three points.
"We have got threats at the top of the pitch now, we looked a threat all night especially in the first half," Wilder said.
"I am proud of the performance. They all put their bodies on the line and you get your rewards and we did that in the form of three big points.
"We were a touch disappointed with the goal they scored on the stroke of half time. We could have crumbled and gone under but there wasn't that in the team.
"We played smart football in the second half. We turned them around and squeezed them in. And in the end I thought we were pretty comfortable and got a deserved three points.
"When you have not won for a while sometimes you can take a backwards step. But we didn't do that - we made positive substitutions and we stuck forwards on because we wanted that third goal.
"But overall it is a big three points for us. It is a good start for me in my managerial career here and I am delighted for the fans who were with us all night.
"We are in a difficult situation and there are difficult hurdles to overcome between now and the end of the season. But we need to give ourselves a chance and hopefully this is a platform for us."
Torquay boss Chris Hargreaves said: "I am not seeking excuses. Yes, we have had three home games in a row postponed and it has been stop-start for the players but the result still reads the same, 2-1 and a loss.
"What we have got to look at are the facts, not the state of the pitch. The facts are that two defensive errors cost us and to concede two goals in the first 16 minutes means you are always facing an uphill struggle.
"Basically we gave ourselves a mountain to climb and for the younger players the game will act as a steep learning curve.
"I am deeply disappointed we lost but I don't buy into the theory that this was a six pointer because you only get three points for a win. Northampton got the win and three points.
"I did not get too high when we won at Pompey and I won't get too down about this. Now we prepare for another challenge another test, at Chesterfield on Saturday.
"There were positives to take from this: Krystian's goal and I thought Jordan (Chapell) was a bright spark when he came on. The main thing is that we must improve, we must get better. It's that simple."
- Sports & Recreation
- Krystian Pearce
- Jordan Chapell
- Emile Sinclair