The visitors scored four tries for a bonus point win, and they are now on 11 points, two clear of the Cell C Sharks, while the DHL Stormers (7) and Vodacom Bulls (5) make up the rear.
While the hosts struggled to find their rhythm, the visitors from Gauteng scored when presented with opportunities, while Fred Zeilinga also had a great day with the boot, contributing 17 points.
The Emirates Lions, whose pack was great in the scrums, started very well and were 10-0 up after 15 minutes, with Horn scoring his first try after a superb run by Vincent Tshituka, while Zeilinga added the conversion and a penalty goal.
The DHL Stormers finally awoke from their slumber with two tries in quick succession – by Stefan Ungerer and Seabelo Senatla – to take a 12-10 lead, but Zeilinga had the final say in the first half with his second penalty goal, the three points putting the Emirates Lions in the lead by 13-12 at the break.
The men from Johannesburg came out firing in the second half and quickly stretched their lead courtesy of tries by Andre Warner and Tshituka, which saw them in command at 27-12 after 55 minutes.
Although the Capetonians scored a third try late in the match by Andre-Hugo Venter – son of former Springbok hard man Andre Venter – the visitors had the final say when Horn went over for his second try, which secured them a crucial and well-deserved bonus pount.
DHL Stormers 19 (12) – Tries: Stefan Ungerer, Seabelo Senatla, Andre-Hugo Venter. Conversions: Manie Libbok (2).
Emirates Lions 37 (13) – Tries: Francke Horn (2), Andre Warner, Vincent Tshituka. Conversions: Fred Zeilinga (4). Penalty goals: Zeilinga (3).