The two-time grand slam winner and Olympic champion appeared on course for certain defeat when he trailed 6-2 in the second set tiebreak, only to reel off four straight points as Robredo tightened when on the brink of victory.
The pair both wasted chances to seal the set as they mixed glorious winners with nervy misses, with Robredo wasting his fifth match point at 7-6, before Murray eventually blasted an unstoppable forehand to take it 11-9 and force a decider.
World number 11 Murray then broke Robredo three times in the third set with the Spaniard, also chasing a first win of the year, appearing hampered by injury as he failed to chase down balls.
The victory at the $590,230 outdoor hardcourt event boosted Murray’s hopes of making a sixth appearance at the season-ending ATP World Tour Finals in London in November after he was forced to withdraw from the event last year through injury. (Reuters)