Muniain won an early penalty and capped the victory with a fine goal after Spain international Fernando Llorente scored twice for the Spaniards.
It was virtually all one-way traffic in the first half, and Athletic wasted no time in launching their first attack with Llorente seeing his long-range effort held by Szabolcs Safar.
They did not have to wait long to make the breakthrough though, with a clumsy challenge from Joachim Standfest bringing down Muniain inside the area, although the defender could feel unlucky to earn a yellow card that would later come back to haunt him.
Llorente stepped up to dispatch the resulting penalty with ease.
Mamadou Diabang had a rare sight of goal for the visitors in the 16th minute, but his shot was pushed clear by Gorka Iraizoz.
Not long later, quick thinking from the hosts earned them their second goal.
Wasting no time in taking a throw-in, Athletic broke down the right and Markel Susaeta's cross set up Llorente for a spectacular half-volleyed finish that left the goalkeeper with no chance.
Diabang brought another save out of Iraizoz, but it was Athletic who went closest to scoring again before the break as Muniain capped a fine move with a right-footed shot that hit the outside of the post.
Athletic continued to attack in the second half, with Francisco Yeste sending an early free-kick narrowly wide.
When the third goal did come, 10 minutes after the restart, Athletic made it look easy.
With players breaking forward in numbers, Joseba Etxeberria knocked a delicate pass through to Llorente who beat the offside trap and then unselfishly passed up a hat-trick to square for Muniain, who passed the ball into the net.
Michael Liendl went straight down the other end for Vienna, but after good build-up play, sent his shot straight at Iraizoz.
The job was done as far as Athletic coach Joaquin Caparros was concerned, with Llorente withdrawn.
Even without their leading striker, Athletic continued to play with real swagger.
Susaeta capped another fine move with a left-footed effort that went narrowly wide of the far post.
Susaeta then tried his luck from 25 yards but the goalkeeper got down to keep the ball out.
The frustration told on Standfest as he slid clean through Muniain to earn a second yellow card and an early shower with 20 minutes to go.
Muniain continued to terrorise the visitors, heading narrowly wide moments later.
Carrion Aitor Ocio flashed a free-kick inches wide, but a fourth goal would elude Athletic.
Vienna kept plugging away, but the closest they came was a snap shot from substitute Thiago Schumacher that was straight at the goalkeeper with 10 minutes to go.