Flyhalf Russell helped to set up four tries, including both Steyn scores, in a 35-7 win at Murrayfield on Saturday (Sunday NZ time) to leave Warren Gatland winless in his second coming as Wales coach.
It was the first time Gatland had lost to Wales in a Six Nations coaching career stretching back to 2007.
It was a record loss to Scotland for Wales, who have now lost 11 of their last 14 matches.
Scotland last won two games in a row in 1996 when the tournament was still the Five Nations before Italy joined the enclave.
Hooker George Turner put Scotland on the board with a first-half try from a rolling maul before being sinbinned for a high contact shot on Wales centre George North.
Wales’ veteran captain Ken Owens put the visitors on the board just before halftime with a try from a lineout maul to cut Scotland’s lead to 13-7.
But right wing Steyn scored a double in the second spell, the first after a delightful dab and clever offload pass by Russell and the second from the flyhalf’s superbly executed crossfield kick
Steyn’s second score came after referee Andrew Brace sinbinned fullback Liam Williams after a series of ruck infringements by Wales.
Substitute fullback Blair Kinghorn clinched the bonus point with the fourth try after more magic from Russell and a storming run by left wing Duhan van der Merwe, who committed the defence before putting Kinghorn clear.
Russell also sparked the move that led to a late try out wide for No 8 Matt Fagerson.
Scotland now join Ireland – who had a 32-19 bonus point win over champions France in Dublin – at the top of the Six Nations standings.
Russell played down his own role as he collected the player of the match award.
“A great game and a great result for us,’’ he told BBC One. “I was just doing my job out there, making other boys look good. We showed the continuity in the squad and our attack had that as well as our defence shutting people out.”