The 23-year-old centre slotted all the points for Glasgow in their 18-3 victory at Cardiff on Saturday which has taken them third in the RaboDirect PRO12.
Horne was handed kicking duties by head coach Gregor Townsend after impressing in training last midweek and he's is hoping he has done enough to stay in the side for Sunday's opening Heineken Cup fixture at Northampton Saints.
He said: "I have been working hard with Duncan Hodge, the Scotland kicking coach, and hopefully that work is starting to bear fruit.
"I slotted one against Zebre at Scotstoun the game before and had a good week with the boot in training and, when Gregor said to me I would be taking the kicks for the Cardiff game, it was a boost.
"To be honest, I made a bit of a haggis of the first one, but the rest went pretty well and I think I only missed the one penalty so that was a fairly consistent performance with the boot.
"It would be massive for me to repeat the role at Northampton on Sunday and hopefully I have done enough to stay in Gregor's plans.
"It was important to keep the momentum going at Cardiff and we did that, and now go into the Northampton game on the back of a four-game winning run.
"For me, it is just great to be getting consistent game time and hopefully I am doing enough to justify my inclusion."
Horne joined Glasgow in 2009 and signed a new contract in 2012 that will keep him with the Warriors until at least May 2015.
But after spending the 2011/2012 season with the Scotland full-time sevens squad, he is now at last making a real impact at Warriors.
Townsend's decision to hand Horne the goal-kicking duties and free up Ruaridh Jackson to concentrate on running the game at 10 proved to be a masterstroke in Cardiff.
Jackson's inconsistency with the boot in front of the posts had a damaging knock-on to the other parts of his game in terms of his handling and positional kicking.
But, relieved of that stress, the stand-off flourished at the Arms Park where he had his best game in a Glasgow shirt this season.
But the centre refused to blow his trumpet and heaped praise on the Glasgow pack who destroyed the Blues front eight with an intimidatingly physical performance which will need to be repeated at the English Premiership leaders on Sunday.
Horne said: "I thought the pack were awesome at the Arms Park.
"Ofa Fainga'anuku was killing people out there with some of his tackles and Chris Fusaro was everywhere.
"At the set-piece we just smashed Cardiff and we are going to need to repeat that level of physicality on Sunday at Northampton.
"But we will be going south with confidence high and determined to get the Heineken Cup campaign off to a winning start.
"It will be a huge challenge to turn Northampton over on their patch, but it is something we believe we are capable of."