The German rider completed the 36.7km course from Real Monasterio de Santa MarÃa de Veruela to Borja in 47min 02sec.
His time was 15 seconds faster than Omega Pharma-QuickStep team-mate Rigoberto Uran and 18 seconds faster than time trial rival Fabian Cancellara (Trek Factory Racing), who was given a seven-second penalty for drafting.
Alberto Contador finished fourth, 39 seconds in arrears, to move into the race lead.
"It was one of the hardest time trials this year," said Martin.
"The mountain was quite hard, it was hard to find a rhythm and still keep some energy for the second part with the descent and the flat sections. It was also technical with a lot of corners. For sure it was a challenge. I also had some issues with heat at the end.
"I wasn't so sure about the win. But I'm super happy I did it, as this is a race that does not suit me perfectly and there are plenty of strong time trialists here at La Vuelta."
The win is a timely confidence boost for Martin ahead of the UCI Road World Championships in Spain at the end of the month.
"I also see that my condition is good and I think this gives me huge morale in anticipation of Worlds," said Martin.
"I have shown I'm heading in the right direction. I wanted to win for the team also. I am thrilled with the fact that we have two OPQS guys on the top two steps of the podium, and even Pieter Serry was 11th. Now we have a victory at La Vuelta and we can look to the next days with Rigoberto Uran on the virtual GC podium. Team spirit is super high."
SBS will broadcast eight live stages of the Vuelta a Espana, in addition to daily highlights.
SBS will have live coverage of the 2014 UCI Road World Championships.