The Blades were 3-0 up at the break after goals from Chris Basham, Stefan Scougall and Keiron Freeman, before a second half treble from Harry Chapman sealed defeat for the O’s.
Cavasin made two changes from the side which lost 2-0 at home to Crewe Alexandra last week with Alan Dunne making his first start of the season and Jay Simpson being recalled to the starting line-up in place of Jens Janse and Jordan Bowery respectively.
After an uneventful first 10 minutes, which saw both sides settle into the game, the O’s created the first opportunity as Sandro Semedo flashed an effort over the bar.
Cavasin’s side built on that and had a gilt edged chance to go in front when Ollie Palmer showed Jake Wright a clean pair of heels but Blades debutant goalkeeper Aaron Ramsdale was able to come out and block the effort behind for a corner.
From that moment on the hosts began to assert themselves on the game and a series of chances came their way.
Daniel Lafferty and Mark Duffy were a common theme for the chances, with the former teeing up the latter to fire over from the edge of the O’s box, before Duffy was denied on the line by Callum Kennedy as he looked to break the deadlock from a tight angle.
Orient had to be thankful for goalkeeper Alex Cisak on 22 minutes as he prodced a fine full-stretch save to deny Duffy’s low shot from just outside the box, however, the hosts were to take the lead within the same minute.
A right-wing ball in from John Fleck found Chris Basham unmarked and the defender was able to apply the finishing touch to put the Blades ahead.
Kieron Freeman then curled an effort wide as they looked to build on their goal, before the O’s were forced into an early change when Ollie Palmer was withdrawn through injury, and on came Jordan Bowery in his place.
O’s mounted a quick counter attack moments later as Simpson played the ball into the path of Massey on the right and after a mazy run his shot was too hot for Ramsdale to handle, before Jack O’Connell was forced to kick the ball out for an Orient throw-in.
But with just six minutes to go before the break the hosts doubled their lead when a Stefan Scougall volley struck the ground and looped its way into the far corner of the net.
And it got worse on the stroke of half time as Kieron Freeman’s header found the back of the net as the O’s found themselves 3-0 down at the break.
Cisak was in action again early in the second half, parrying a Duffy effort wide before also tipping a header over the bar, though a fourth came eight minutes into the second half when Harry Chapman’s shot across goal found the corner of the net.
Nigel Atangana looked to pulled one back a minute later but skied his effort high over the bar, before Dunne’s low effort was comfortable for Ramsdale in the Blades goal.
Cisak on the otherhand was kept busy and saved a Lavery shot with his legs after the O’s lost possession in their own half, before the hosts added a fifth as Chapman scored his second of the game when getting on the end of a right-wing cross.
Second half substitute Paul McCallum headed over from Massey’s right-wing cross but that was as good as it got for the O’s in the second half.
Five became six in stoppage time as Chapman made the most of a slip up at the back and the striker coolly chipped Cisak to round off a miserable afternoon.
Sheffield United: Ramsdale, Wright, Basham, O’Connell, Freeman, Coutts (Whiteman 73), Duffy (Brooks 60), Fleck, Lafferty, Scougall (Lavery HT), Chapman.
Subs: Long, Sharp, Brown, Reed, Whiteman.
Goals: Basham (22), Scougall (39), Freeman (45), Chapman (54, 69, 90+2).
Orient: Cisak, Dunne, Hunt, Parkes (Janse 80), Kennedy, Massey, Atangana, Weir, Semedo, Simpson (McCallum 70), Palmer (Bowery 35).
Subs: Sargeant, Collins, Pollock, Benedicic.
Booked: Massey (74)
Attendance: 6,099 (316 Leyton Orient fans)
Referee: Nigel Miller