Rovers produced a fine second half display to earn another big Carabao Cup win and progress to round three of the competition.
There were four goals on the night, by a quartet of scorers, with Joe Nuttall getting things going in the first half and Danny Graham, Paul Downing and Kasey Palmer completing the rout in the second.
It was a much improved second half performance after the teams went in level at the break after Joan Luque levelled things up midway through the first half.
But in the end, Rovers ran out comfortable winners to continue their unbeaten start to the 2018-19 campaign.
Joe Grayson became the first player to follow in his father's footsteps in making a senior appearance for Rovers since Wilfred Crompton in 1929.
The Academy graduate earned the nod for his first ever Rovers start, with dad Simon playing 35 times for us between 1999 and 2002.
Grayson was one of six changes, with Downing, Craig Conway, Lewis Travis, Paul Caddis and Graham all coming into the side for the Carabao Cup clash against the Imps.
Nuttall continued his run in the Rovers side with a second consecutive start and it was he who got Tony Mowbray's side off to the perfect start as he opened the scoring just five minuted into the encounter.
The young frontman lashed home at the second attempt after Jason Shackell had originally blocked his first attempt, which fell nicely back to the Rovers number 24.
Lincoln searched for a response and soon after Nuttall's opener, Luque fired an effort from range well wide of David Raya's left-hand post.
Luque was again involved in the next chance on 14 minutes as Michael O'Connor picked him out with a lovely diagonal ball which caught out Caddis, but Raya was on hand to beat away his countryman's near post effort.
At the other end, Graham latched onto Caddis' low pull back but saw Shackell in the way to flick his first time strike off for a corner in a lively opening 20 minutes.
Luque was causing problems down the Rovers right and this time the battle of the Barcelona-born boys was won by the Lincoln man as he beat Raya with a thumping strike after getting on the end of a Matt Rhead flick on just before the half hour mark.
Nuttall almost start the second half as he did the first - with a goal - but somehow he skewed a header just wide after a lack of communication in the visiting backline.
But that goal did come a moment later as Travis' fine run and pass found Graham, who cooly slotted low to beat Slocombe and find the corner.
It was a good start to the half and Joe Rothwell almost added to the tally a minute later but blazed an effort into the Blackburn End.
Rothwell went close again just before the hour, with his strike from range forcing Slocombe into action by diving down low to stop the shot.
But a moment later that third goal did come as Downing got on the scoresheet for just his second ever Rovers goal and it came in really composed fashion.
A corner was cleared as far to Caddis, who spotted the lurking Downing on the edge of the box and the defender slotted home into the corner for his first goal since November 2017 at Blackpool.
Rovers were continuing to probe and Conway almost produced the spectacular with his curling effort dropping just wide of the target with 23 minutes remaining.
Dan Butterworth was the latest Academy graduate to earn his first senior appearance as he replaced Graham with 19 minutes remaining and the young forward went close a moment later, with Slocombe equal to his powerful drive.
But Slocombe could do nothing soon after as Palmer produced the spectacular; curling home a free kick into the top corner from all of 22 yards to turn 3-1 to 4-1.
And that was to be the last notable action of the game as Rovers ran out comfortable winners at Ewood.
Rovers: Raya, Nyambe, Downing, Grayson, Bell, Caddis, Rothwell (Palmer, 60), Travis (Tomlinson, 80), Conway (c), Graham (Butterworth 71), Nuttall.
Unused substitutes: Leutwiler, Smallwood, Lenihan, Bennett.
Goal: Nuttall, 5, Graham, 50, Downing, 60, Palmer 76
Lincoln City: Slocombe, O'Connor (Pett, 63), Shackell, Rhead (c) (Akinde, 62), Green, Chapman, Wilson, Luque (Andrade, 63), Crookes, Eardley, Anderson.
Unused substitutes: Gordon, Frecklington, Toffolo, Smith.
Goal: Luque, 28
Booked: O'Connor, 52
Attendance: 5,211 (1,214 away)