The pair combined to create what proved to be the game's winning goal on 41 minutes. Matthews, who returned to the squad in place of the injured Kwesi Appiah, threaded an excellent through ball for Nichols to finish with aplomb for his second goal in four games.
The Reds have now won their last three League Two games in a row. Crawley's victory also brought an end to the third-placed Cobblers' five-game winning run at home.
Yems said: "I've told that ones that haven't been playing to do their jobs and you've got to be fit enough and ugly enough to come in and do a job.
"We had one moment of really good play, Sam has played Tom in and he's scored, but the rest of it is digging in.
"It's what they do and it's what Sam does. He can open things up.
"Tom has had a couple of games where he hasn't scored but that's what he's got in his locker. That's why people look at him and say what a good player he is.
"But Tom knows that, I know that, hence why he is here. It doesn't half take the pressure of you when you have players like that can score. Let's just hope he gets a few more."
Despite sitting in the League Two promotion places, the hosts failed to threaten until the final 15 minutes.
Northampton debutant Chanka Zimba cracked the crossbar, Aaron McGowan narrowly fired wide, and Reds keeper Glenn Morris superbly denied Zimba when put through one-on-one at the death.
Yems was absolutely delighted with the performance of the Crawley back three, but admitted his side weren't at their best at Sixfields..
He added: "You've got them boys at the back now, Tony [Craig] and Lynchy [Joel Lynch], they've had careers but they've done it a high levels and it rubs off.
"You've got young Ludi [Francillette] the other side, and he's never experienced anything like this.
"It wasn't the best. We've played a lot better in the past and got beaten.
"When we've got 19 members of staff and players that have got Covid, and you've got injuries, and you're trying to get people in positions and they don't go, it's hard.
"But if you've got the heart and the desire to win games it helps.
"Fair play to Northampton. How they didn't score today I don't know, but then it was good from us, and there was a good save by Glenn.
"I think Nico's goal, from where I was, I don't know how he scored it to be quite honest with you. It was a little bit of magic."
Victory at Northampton has pushed the Reds up to 11th, just four points shy of the play-off places. But Yems was uninterested in talk of a late promotion charge.
He said: "You can look at what you want, but for me I don't look at the table until April or May."