A perfect day for Matthews' Orica-GreenEdge team resulted in the 23-year-old getting the better of both Garmin-Sharp's Martin and Spaniard Joaquim Rodriguez (Katusha) on the ramped finish in Arcos de la Frontera after a rolling 198-kilometre stage from Cadiz.
Matthews now tops the overall standings by four seconds over race favourite Nairo Quintana (Movistar) after pocketing 10 bonus seconds over the finish line.
It was a case of job-well-done for Orica-GreenEdge who controlled the stage from the outset, reeling in the day's break before setting up their man for the third Vuelta stage win of his career.
Having suffered the demoralising setback of being forced to sit out the Tour de France while in the form of his life owing to a freak training accident, Matthews has now repeated the success of his Giro d'Italia back in May - where he won a stage and wore the leader's pink jersey.
It was Martin - responding to an early surge by Italian Damiano Caruso (Katusha) inside the final kilometre - who looked to have the win in the bag before Matthews timed his jump to perfection, zipping past the Irishman as the road flattened out to leave the Irishman thumping his handlebars in frustration.
Making his own Grand Tour comeback after crashing out in the opening team time trial of the Giro in Belfast, Martin was forced to settle for second place ahead of Rodriguez, with Belkin pair Wilco Kelderman and Paul Martens completing the top five.
Sunday's stage two winner Nacer Bouhanni (FDJ) came an impressive eighth while there were top 10 finishes for both Cadel Evans (BMC) and Chris Froome (Team Sky).
Matthews seized the red jersey from the shoulders of Movistar's Alejandro Valverde after the Spaniard was caught out in a split and lost seven seconds at the finish. Valverde is now third in the overall standings, 11 seconds down on the Australian.
Britain's Froome will consider himself lucky when both he and Bouhanni narrowly avoided hitting the deck with 20km remaining when two Movistar riders - Jonathan Castroviejo and Adriano Malori - crashed into the barriers while picking up a musette.
FIVE-MAN BREAK: Once again, South African Jacques Van Rensburg (MTN-Qhubeka) was part of the day's main break after attacking with Danilo Wyss (BMC), Luis Mas Bonet (Caja Rural), Jonathan Fumeaux (IAM) and Jerome Cousin (Europcar) just 13km into the stage, which started on the deck of aircraft carrier Don Juan Carlos in the port of Cadiz.
With the break establishing a maximum lead of eight minutes, Frenchman Cousin picked up maximum points on the first of two Cat.3 climbs before Switzerland's Fumeaux - clearly struggling in the sweltering 35-degree heat - became the first of the escapees to drop back.
Spaniard Mas Bonet surged clear of the other three leaders with 70km remaining to cross the next two summits in pole position and take the polka dot mountains jersey. Mas Bonet was the last of the escapees to be caught by the peloton, finally throwing in the towel inside the final 30km.
Australian Adam Hansen - riding his tenth consecutive Grand Tour - had a dig on an uphill rise with 17km remaining, but the Lotto Belisol rider was soon reeled in despite pulling out a 22-second gap.
RIDE OF THE DAY: Orica-GreenEdge, who rode consistently on the front of the peloton to help reduce the gap of the break before setting up their man Matthews with aplomb.
DAY TO FORGET: On Sunday he was in the red leader's jersey but on Monday Jonathan Castroviejo was picking himself up off the tarmac having hit the deck after bungling a musette pick-up from one of his Movistar soigneurs.
Third in the Tour de France, Thibaut Pinot (FDJ) shipped another four minutes as he confirmed he is in Spain very much for mountain stage wins as opposed to the GC, while Australian youngster Rohan Dennis (BMC) showed he's perhaps not ready to take over the mantle from veteran team-mate Cadel Evans after the rookie rider - second in the Tour of California earlier in the year - finished last, 4:34 down on Matthews.
COMING UP: Tuesday's 165km stage four from Mairena del Alcor to Corduba includes two categorised climbs but should conclude with a bunch sprint with a slightly uphill finish. Bouhanni at the double?
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- Tour de France
- Cadel Evans
- Jonathan Castroviejo