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A superb leadout from teammate Rui Oliveira delivered Molano in perfect position for the win, the Colombian launching with clean air in the final metres to cap a UAE Team Emirates masterclass in Zaragoza.
Groves endured a late mechanical and found himself boxed in around the final corner, finding the space to jump out and contest the sprint but with not enough road to catch Molano, the Aussie forced to settle for second as Boy van Poppel (Intermarche-Circus-Wanty) rounded out the podium.
It was the second near miss in a week for Groves to take his third win, banging his handlebars in disappointment at the finish in similar fashion to his earlier loss to Geoffrey Soupe (TotalEnergies) in Stage 7.
The Queenslander did extend his lead to 118 points in the green jersey though, taking maximum points in the day's intermediate sprint which also featured some GC action as Primoz Roglic (Jumbo-Visma) was a surprise second to nab four bonus seconds.
Aside from Roglic's smart sprint foray the overall rankings went unchanged, the peloton content to coast and take advantage of the flat parcours with a daunting journey to the Col du Tourmalet looming.
The 151 kilometre stage was largely uneventful, the breakaway of the day forming two kilometres in as Jetse Bol (Burgos BH) and Abel Balderstone (CAJA Rural-Seguros RGA) made their way off the front, allowed to stay away by the peloton before being swallowed up with 43 kilometres to go.
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Daily Highlights: Stage 12 - La Vuelta a Espana 2023
Alpecin-Deceuninck controlled the bunch throughout the day on the front, keeping Groves safe, before Bahrain Victorious and EF Education EasyPost came to the fore as the pace quickened into the finale.
Groves looked to have another perfect situation inside the final kilometre, nestled in the wheel of two teammates at the front before Oliveira and Molano used the last left-hand bend to snatch the wind and box the Australian in.
Oliveira turned on the afterburners out of the corner, dropping Molano off in the final 100 metres to give the Colombian an easy sprint to the line, Groves' foot slipping from his pedal and affecting his sprint to come around.
La Vuelta moves into Tour de France territory tonight with a stage featuring 4,000 metres of climbing and a summit finish on the mythical Col du Tourmalet. Watch the action LIVE from 9:40pm AEST on SBS On Demand before coverage on SBS VICELAND begins from 10:40pm AEST.