GLASGOW, Scotland (AP) Andy Murray sent Britain into its first Davis Cup final in 37 years on Sunday, securing victory over Australia with a straight-set win over Bernard Tomic.

Despite struggling with a back injury and coming off a five-set doubles match on Saturday, Murray managed to find another peak performance to beat Tomic 7-5, 6-3, 6-2.

That, coupled with Murray's win over Thanasi Kokkinakis on Friday and his doubles triumph with brother Jamie, gave Leon Smith's team an unassailable lead. Kokkinakis later beat Dan Evans 7-5, 6-4 in the meaningless fifth match to make the final score 3-2.

Belgium awaits Britain in the Nov. 27-29 final after beating Argentina by the same score in the other semifinal.

Now Murray has barely two months to ensure he is fully fit to help Britain win the Davis Cup for the first time since 1936.

''My back has been giving me a lot of trouble this week,'' the third-ranked Murray said. ''It's nothing to do with the previous issues I had with my back, it's a completely different thing.

''My back was absolutely fine during the U.S. Open, then I took five days off, started practicing again on Sunday here ... and then on Tuesday night my back was extremely sore and got progressively worse the next couple of days.''

But just as he was during Friday's demolition of Kokkinakis, Murray was in top form as he treated about 8,000 fans at the Emirates Arena to an outstanding array of shots.

The Scotsman has now helped the British to their last seven Davis Cup points - along with Jamie Murray - to see off the United States, France and now Australia.

Murray had endured four hours on court alongside his brother before seeing off Lleyton Hewitt and Sam Groth in Saturday's doubles, but he could not have started any better as he launched two aces on his first three points.

Murray only lost one point in his first two service games and broke in Tomic's second, winning his third break point when a deep, high shot put the Australian on the back foot before he sent a backhand into the net.

It was not entirely plain sailing. Murray was broken as he served for the set to hand his 23rd-ranked opponent a way back, but set up three break points in the next game and finished Tomic off with a deft backhand drop shot.

Murray broke again in the fourth game of the second set as his opponent sent a backhand into the net, and Britain's top-ranked player went on to serve out the set at love.

In the third, he broke twice and wrapped up the victory when his opponent sent a return wide.

Britain's last final appearance was in 1978.