After losing the opening Test, the world champions bounced back to claim the remaining matches as the Lions will head home licking their wounds.
Cheslin Kolbe scored South Africa’s only try while Handre Pollard added eight points and Steyn kicked two penalties in the latter stages in Cape Town.
For the Lions they crossed through Ken Owens while Finn Russell slotted a conversion and three penalty goals, but the touring outfit came up short.