The Lions were put to the test when Poite whistled another penalty within kicking range off a maul and the Wallabies were down by just three points six minutes into the second half.
However, another dominant Lions scrum gave Halfpenny his sixth successful kick to give the tourists some breathing space at 22-16 after 51 minutes.
Sexton kicked the Lions away when he scored a converted try off a Halfpenny pass in the 56th minute and the tourists were in the box seat at 29-16.
The winning break came when Halfpenny fielded Genia’s clearing kick and launched a counterattack, beating the tackles of Genia and Joe Tomane, to send winger George North racing over for an unassailable 34-16 lead.
And Jamie Roberts, a controversial replacement for the dropped O’Driscoll, vindicated Gatland’s selection when he arrowed through for the final try with 11 minutes to go.