Rob Baxter's side collected their second win in three starts this term on Friday night as Steenson led the way in a 25-22 victory over Gloucester at Kingsholm.
The Irish playmaker provided 14 points with the boot as Devon's finest won away to the Cherry & Whites for the third time in four seasons.
The hard-fought win momentarily lifted the Chiefs to the summit of the Premiership for the second time this season, but weekend wins for the likes of Bath, Saracens and champions Northampton Saints saw Exeter drop to fourth ahead of this Sunday's encounter with Harlequins at Sandy Park (2pm).
Steenson knows a similar display - if not better - will be needed to sink the visiting Londoners, who themselves returned to winning ways last weekend when they defeated visiting Wasps at the Twickenham Stoop.
“Friday was a good all-round performance, there are still a lot of things to work on, but it was a good win away from home,” said Steenson.
“Kingsholm is a fabulous place to play, and there is nothing better than coming here and walking over to our fans at the end of the game with an away win and seeing the amount of support we have in the Shed, and everybody so happy and giving the Tomahawk Chop.
“It was a big effort from the boys. We were in control for large parts of the game, but a couple of bits of indiscipline seems to be our Achilles heel at times, and we let them back into it, but the boys weathered the storm really well, and we were really pleased to come out on top in the end.”
The Chiefs suffered an early blow when winger Ian Whitten was sin-binned for a dangerous tackle on opposite number Charlie Sharples. And whilst the Ulsterman was sidelined, Exeter conceded 12 points, including tries for Jonny May and Dan Murphy.
However, Steenson - who was later named man of the match by the BT Sport pundits - helped kick his way back into contention and by the break the visitors were in control 22-12 thanks to his boot and a try from flanker Ben White.
“We showed good composure in the first half, did the things we had talked about doing, and taking the points when they were on offer,” explained Steenson.
One of the key features of Exeter’s second-half display was their defence, as they withstood most of what a fired-up Gloucester could throw at them.
“It is something we have been working hard on and really pride ourselves on,” said Steenson. “The physicality, and putting the line speed on sides, and even though it is tough to play like that, it is tough to play against it as well.”