Saracens losing to London Irish earlier in the day opened the door for Northampton, and a late try from George Pisi, converted by fly-half Stephen Myler, meant they achieved their goal in wet and windy Devon.
"It was a very hard-fought win in difficult conditions," said Mallinder. "We were pretty pleased with ourselves at half-time having played into a gale and scoring two good tries.
"Any win away from home is a good win. Exeter are a good side and they will beat a lot of good sides here as well.
"I think that we probably let Exeter back in to the game in the second half and a lot of credit to them because they played some good rugby in those conditions which put us under pressure.
"To score the winning try with a couple of minutes to go was outstanding. We knew that we would have to play for 80 minutes to match Exeter and we trusted our defence.
"We could have easily lost this game but we stuck at it and I am really pleased with the belief of the side. We are in a good place at the moment, internationals doing well for England and Wales and then the lads back at home."
Northampton are also through to the semi-finals of the LV= Cup where they will host Saracens next month, plus the quarter-finals of the Amlin Challenge Cup where they have a trip to Sale Sharks in April.
Mallinder added: "This is where we want to be and I think any team wouldn't want to be out of competitions as it is only February. There is still a lot of rugby to go and we haven't got the biggest of squads so we have to look after and manage the players.
"We have always said that we can't worry too much about other people but of course you do look at results and see what is going on with Saracens losing. But the pressure comes back on with Bath winning and they are creeping back towards you."
Saints had a slender 10-9 lead at the break through a try from lock James Wilson and Samu Manoa with the Chiefs replying as Gareth Steenson, with the wind at his back, landed three penalties.
Exeter dominated the early stages of the second half and scrum-half Dave Lewis crossed for the Chiefs' only try, converted by Steenson. Yet the visitors snatched the game with their late show.
Exeter had to settle for a losing bonus point to leave them eighth in the table, with matches to come at home to Bath, away to Saracens and then London Irish before an LV= Cup semi final at Bath.
Exeter head coach Rob Baxter said: "I'm a bit frustrated because ultimately I don't think that we played very well particularly in the first half.
"I don't think that we were really as physically aggressive as you need to be when you play a side like Northampton.
"We look back [on the game] and most of it will be okay for 90 per cent but there are too many of those odd things that are hurting us when we need to be well focused and need to be really decisive about what we do.
"I told the guys that we have let one slip through our fingers because if we had played in the first half anything like we did in the second we would not have been behind and we wouldn't have conceded the points that we did."
- Sports & Recreation
- London Irish