The Spanish defender had already fired Wednesday level in the 68th minute when diverting the ball home from close range, and with the scores level at 2-2 heading into time added on, he pounced again from a rebound in the penalty area to grab the winner.
Goals from Millwall pair James Henry and Liam Trotter had given the visitors a 2-1 half-time lead after Owls winger Jermaine Johnson had put Jones's side ahead.
But Llera was the hero as Wednesday maintained their unbeaten start in the npower Championship following promotion in May.
Millwall midfielder Henry pulled the first chance of the game wide when well-placed inside the penalty area in the fourth minute, while Wednesday responded through winger Johnson, who thumped a 20-yard drive straight at visiting goalkeeper Maik Taylor.
Johnson cut in from his wing again to fire another angled effort wide soon after and, after Millwall had failed to heed the warning, the Jamaica international took advantage to blast the Owls into a 19th-minute lead.
This time drifting in from the left, Johnson took aim from the edge of the penalty area and found his range with a right-footed rocket which flew into the top corner.
Millwall wasted a gilt-edged chance to equalise soon after when defender Karleigh Osborne lashed a volley over the crossbar from 12 yards.
But 10 minutes before the break the Londoners were back on level terms. Striker Andy Keogh played the ball across the area from the right and Henry buried the ball into the top corner.
Wednesday midfielder Rhys McCabe's 20-yard effort was comfortably held by Taylor before the home side were rocked by Millwall's second.
Defender Alan Dunne this time supplied the cross from the right and Trotter applied a carbon-copy finish, slamming the ball beyond static Owls goalkeeper Chris Kirkland into the roof of the net.
Wednesday stormed out of the blocks at the start of the second half, winger Michail Antonio crashing a shot over the crossbar from the edge of the area, while Taylor kept out another angled effort from Johnson.
The home side laid seige on the Millwall goal for the next 15 minutes and after substitute striker Chris O'Grady's point-blank effort was brilliantly held by Taylor, the Owls finally forced the equaliser.
Antonio whipped in the ball in from out wide and central defender Llera stuck out a long leg to divert the ball home from six yards.
But Wednesday continued to swarm forward in search of the winner.
O'Grady, a 58th-minute replacement for Gary Madine, and new Spanish striker Rodri both fired in shots in quick succession before the latter volleyed over the crossbar.
As the game headed towards stoppage time O'Grady's shot following McCabe's free-kick was blocked by Lions defender Osbourne and when the ball broke loose six yards out, Llera lashed home the winner into the top corner.