It set up a crunch Pool A showdown with host nation Japan for a place in the Rugby World Cup quarterfinals.
Horne scored his first two tries from scrumhalf and added a third from the left wing as Scotland finally got their high-octane running game going in their third match in Japan.
Flyhalf Adam Hastings, son of Scotland great Gavin, also made a significant contribution with the first two tries in four first-half minutes and eight conversions for a personal haul of 26 points.
Horne actually crossed for what seemed like a Scottish record-equalling fourth try only for referee Wayne Barnes to call it back for a forward pass.
"That's stage one of a two-stage week completed," Scotland coach Gregor Townsend said. "As an all-round team performance, it was excellent."
Neither Horne not Hastings are likely to start in Yokohama on Sunday when the Scots take on Japan almost certainly needing to record a victory and deprive the hosts of a bonus point to progress to the knockout stages.
"It'll be huge, our focus now is on recovery, making sure we get our preparation right for that game, and our selection," Townsend added.
"We've watched a lot of Japan, and I know they've watched a lot of us too.
"We've just got to make sure we deliver our best performance - we'll have to because Japan are a very good team."
TYPHOON CONCERNS
That match in Yokohama, however, is in danger of being disrupted by Typhoon Hagibis, which is projected to strike the Tokyo area on Saturday, bringing strong winds and heavy rain.
Tournament rules state that any pool game that cannot be played is not rescheduled and instead is recorded as a 0-0 draw, with no bonus points available.
Scotland made 14 changes from the team that beat Samoa 34-0 and many of the players had a dual goal of winning the game as well as trying to force their way into consideration for Sunday's match.
Scotland's scoring in the first half came in an eight-minute burst with Hastings crossing twice, while Horne intercepted a flat pass by Dmitry Perov on his own tryline to give Scotland a 21-0 lead at the break.
Horne then secured the bonus point after a brilliant weaving run of more than 60 metres from Darcy Graham, who was the only player who also started against Samoa.
Russia then ran out of steam and their defence faltered as they missed 41 tackles with hooker George Turner and winger Tommy Seymour crossing before Horne completed his hat-trick with more than 20 minutes remaining.
Match captain John Barclay brought up the half century, just the 13th time Scotland have surpassed 50 points in tests, when he burst free with about five minutes remaining.
"We enjoyed that one, sometimes those games can get a bit scrappy," Barclay said.
"We were a bit nervous about this game having seen what Russia did to other teams at the tournament but we prepared well, we were very professional, played the game we wanted to play and came away with a good result."
Squad captain Stuart McInally completed the scoring, although Hastings did cross after the gong only for Barnes to again rule the try out.
"Scotland were quick and fast and had studied us well, they played well," Russia coach Lyn Jones said. "We were hoping to finish with a flourish but so be it."
