Chelsea will take a slender one-goal advantage into the FA Youth Cup second leg in three weeks time after Rovers were defeated 1-0 Ewood Park.
A first half header from Fikayo Tomori proved to be the difference between the two sides in a tight encounter at Ewood Park.
The visitors edged the opening 45, but after Tammy Abrahams struck the post for Chelsea in the second, it was Rovers who were the dominant side.
But the closest they came to getting a deserved equaliser was 13 minutes from time as Lewis Mansell saw his shot cleared off the line, before substitute Tre Pemberton was denied by a spectacular save on the follow-up.
The two sides will meet again at Stamford Bridge on April 8th, Rovers can go there encouraged with their showing, particularly in the second half.
Billy Barr made two changes from the side that had knocked out Luton Town in the previous round as they welcomed Willem Tomlinson and Joe Grayson into the starting XI. And it was a hardworking Rovers who enjoyed the better of proceedings in the opening exchanges at a chilly Ewood Park.
However as the half wore on it was the highly-fancied Chelsea who started to impose themselves, defender Jake Clarke-Salter narrowly heading over a corner from Mukhtar Ali on 20 minutes.
Then a series of free-kicks given away by the Rovers eventually proved costly as the visitors took the lead six minutes later.
After Tomlinson had needlessly fouled Kyle Scott on the left touchline, Isaac Christie-Davies sent a teasing ball into the box which was glanced home by Tomori to put the pre-match favourites in front.
After going behind the home side struggled to get to grips with their opponents, Andy Fisher in the Rovers goal claiming a cut-back from the lively Dujon Sterling to ensure they trailed by just the one goal at the break.
Like the first half it was Rovers with the impetus at the start of the second, with Matty Platt going close from a Grayson corner kick, but the defender planted his back-post header narrowly over the bar.
But Rovers were then dealt a blow as captain Scott Wharton was unable to continue. Tyler Magloire on as his replacement at the heart of the defence.
The young centre-half immediately called into action with an important clearance as striker Tammy Abraham threatened, but the Chelsea frontman would be a whisker away with the next chance of note just past the hour.
After Lewis Hardcastle was adjudged to have brought down Ali on the edge of the box, Abraham took the free-kick himself, but as Fisher watched on flat-footed, he was fortunate to see the shot strike the post and bounce across the area to safety.
A second change soon followed for Rovers as Tre Pemberton, the fifth round match-winner against Aston Villa, replaced Grayson.
But as Fisher claimed an effort from Ali as Rovers failed to clear their lines, immediately play went up the other end with Joe Rankin-Costello seeing his shot blocked and Lewis Mansell could only find the side-netting on the follow-up.
But 13 minutes from time came the chance for Rovers to get something on the night that their display merited.
As Mansell was slipped in on the right of the area his shot beat Baxter in the Chelsea goal but Tomori got back to clear off the line. The ball went as far as Pemberton who struck goalwards only to be denied by the keeper's acrobatics.
Two of Chelsea's subs then combined as they looked to hit Rovers on the counter, but as Jacob Maddox squared for Ike Ugbo, but his low shot was easily claimed by Fisher.
That would prove to be their only effort of note as Rovers continued to press and probe as the game entered the closing stages. Urged on by over a 1000 fans Barr's youngsters forced a series of late corners but they were unable to get a deserved equaliser.
So it's Chelsea who take a slender advantage into the second leg in three weeks time, but there's still plenty of life left in this tie as Rovers' performance certainly showed.
ROVERS: Fisher, Nyambe, Platt, Wharton (c) (sub Magloire 55 mins), Askew, Hardcastle, Rankin-Costello, Tomlinson, Howarth, Mansell, Grayson (sub Pemberton 67 mins).
Subs not used: Travis, Ascroft, Steer.
CHELSEA: Baxter, Grant, Tomori, Clarke-Salter (c), Chalobah, Sammut, Sterling, Ali, Abraham (sub Ugbo 72 mins), Scott (sub Maddox 61 mins), Christie-Davies (sub Mount 84 mins).
Subs: Cumming (GK), Nartey.
Goals: Tomori 26 mins.
Booked: Ali 86 mins.