Busquets was on the receiving end of a heavy challenge from Gonzalo Escalante and left the field on a stretcher after 10 minutes, but Luis Enrique's men overcame a rough opening to lead through Denis Suarez – who was able to celebrate his first goal for the club having replaced the Spain international.
The second, third and fourth goals arrived after half-time from more familiar sources.
Lionel Messi continued his imperious recent form with his 28th of the season five minutes after the break and Luis Suarez capitalised on a dreadful error from Florian Lejeune to make it 19 for the campaign.
Neymar has not been as prolific as his illustrious attacking colleagues this term but scored for the first time in LaLiga since October when Eibar were picked apart on the break in stoppage time.
Luis Enrique headed into the match without captain Andres Iniesta and lost another midfield talisman when Escalante clattered into Busquets' ankle.
Barca immediately appeared more vulnerable in his absence and when Jeremy Mathieu ceded possession, Eibar midfielder Adrian forced a sharp save from Marc-Andre ter Stegen.
But Barca began to hit their stride, with Messi usually the chief protagonist. He hurdled a lunging tackle from Lejeune to win a free-kick and force Yoel to push his bouncing strike to safety.
At the end of a wonderful 31st-minute move, Messi had a shot blocked but Denis Suarez was on hand to drill superbly into the bottom-left corner from 20 yards.
Neymar and Arda Turan saw close-range efforts blocked by Yoel, with Messi the provider on both occasions and, after Luis Suarez collected Jordi Alba's brilliant pass down the left to strike the inside of the far post, Eibar were grateful to hear referee Jose Maria Sanchez Martinez blow up following one of three stipulated added minutes for half-time.
Messi predictably took centre stage five minutes into the second period as he drove forward from midfield and found Luis Suarez on the right.
Yoel darted out towards the Uruguay's curling ball to the far post but Messi was unruffled and slotted a half-volley nonchalantly home.
Adrian thought he had the hosts back in the match shortly afterwards when he headed in from Pedro Leon's cross, but a marginal offside call went against him.
An over-hit back pass from Denis Suarez caused complications for Ter Stegen, who pushed Ander Capa's spinning effort away from his bottom-right corner, although Lejeune would undo Eibar's good work in the 68th minute.
The centre-back hesitated on the ball and crumpled to the floor under pressure from Luis Suarez, who tore clear to finish clinically.
Neymar was denied a glorious fourth having danced around Yoel, only to be greeted with an erroneous offside flag.
Eibar retained their attacking intent, with Ter Stegen needing a strong arm to keep out a Leon piledriver, but that ambition gave Neymar the chance to add a fourth and cap an impressive display.