Exeter have extra motivation to succeed in the competition this year as the final will be staged at Sandy Park.
And they made the perfect start in their opening match against Quins, with debutant Ceri Sweeney kicking four penalties as well as a conversion from Sireli Naqelevuki's try to seal a comfortable victory.
Hunter, who alongside skills coach Ricky Pellow have taken command of the Chiefs for the next fortnight, said: "It was an excellent way to start the LV= Cup.
"It was a really good performance, tough as well, and that has been the feature of our game over the past couple of weeks that we have defended quite well.
"It was good to see some of the young lads back on the pitch plus a number of guys back from injury. I thought that Quins came and really attacked us with their backs being electric every time they got the ball so it really tested us.
"I think that you have to take your hat off to Ceri, who has been a great guy since he joined the club. He has been a brilliant guy around the squad and he led the team really well and played well too.
"We had a lot of guys who were playing their first rugby for a while so it took time to come together but we started to put some phases together, keep good pressure and we have some exciting players here.
"It is key that we enjoy this for the next few days and then crack on in to Bath as we are all really excited to get to that next Sunday."
The Chiefs had a slender 6-5 lead at the break thanks to two penalties from skipper Ceri Sweeney, with Quins replying with a touchdown from former England wing Paul Sackey.
Quins looked on course to score a second try on the half hour when full-back Charlie Walker made a break with a two on one situation.
But the England U20 was bundled to the ground by opposite number Luke Arcott, a tackle that earned the ire of Quins director of rugby Conor O'Shea.
He said: "Nothing was being given (by either side) in the first half but I thought that tackle was disgraceful. I would need to look back at the incident, but there was no arms, it was late but nothing was picked-up."
Sweeney added two further penalties in the second half plus the conversion of the Chiefs only try on the hour from centre Sireli Naqelevuki.
Quins piled on the pressure in the final 10 minutes but were unable to add to their score.
"A lot of young guys will have learnt well from this game because this (Sandy Park) is a tough place to come and the atmosphere was cracking for the first round of the competition," added O'Shea.
"We just gave them too much ball and played in the wrong half but that is all part of trying to develop and learn. We made too many errors in the first half but any time that we held the ball we looked threatening.
"Their defence was excellent - they are a good side - but we were too inaccurate and we didn't hold on to the ball enough. This is a strange competition because we are not out of it so we have to do a job on Friday night at home to Sale Sharks."