Giroud delivered left-foot, right-foot and headed finishes for the perfect treble - and then whipped a spot-kick into the top corner for good measure.
Chelsea will host Krasnodar at Stamford Bridge next week, but sealed top spot with their win in Spain, and a potentially easier tie in the last-16.
Giroud put the squeeze on Blues boss Frank Lampard to hand the France striker a Premier League start against Leeds on Saturday, once again proving his clinical credentials.
The 34-year-old's added-time header dug Chelsea out of a hole in Rennes last week, with the Blues snatching a 2-1 win at the death in France.
And the former Arsenal player thrived again in midweek European action at the Ramon Sanchez Pizjuan Stadium.
World Cup-winner Giroud could consider a move away from Chelsea in January in a bid to cement his place leading France's attack at next summer's European Championship.
Lampard is desperate to keep Giroud at Stamford Bridge, admitting last week in the wake of that late winner at Rennes that he remains central to his plans.
But Giroud has slipped behind Tammy Abraham and £53million summer arrival Timo Werner in the pecking order of Chelsea's strikers.
Lampard made nine changes to take on Julen Lopetegui's Sevilla following Sunday's Premier League stalemate against Spurs.
And the west Londoners fully vindicated that rotation - most of all Giroud - as Chelsea extended their unbeaten run to 15 matches in all competitions.
Additional reporting by PA.