The young Rovers rallied well after going behind early on to lead at the break, but four unanswered strikes in the second half saw the visitors run out comfortable winners.
Rovers found themselves a goal down just five minutes in but they fought back well, Jordan Preston equalising on 23 minutes after good work from Yeray Torres and Callum Harris.
Just before the break Rovers took the lead from the penalty spot when Liam Langford's barnstorming run from his own half saw the defender upended in the box.
Preston took the spot kick and made no mistake for his 7th of the campaign.
For an hour Rovers were good value for their lead, but two goals in quick succession from Chelsea saw the visitors regain their advantage and this time they didn't let it slip.
Sam Joel went close to making it 3-3 but his well struck shot hit the crossbar.
As the game entered the closing stages Chelsea's calibre showed as they scored two further goals to claim all three points.
"For an hour we did really well, we more than matched them but their extra quality told in the end," said coach David Lowe. "You could argue that we didn't deserve to lose 5-2.
"It is a really good learning curve for the players, playing against this type of top opposition week in, week out.
"It is good for their development, they know how far they have to go to get to that standard."
ROVERS: Williams, Anderson (sub Pierce 84 mins), Langford, Butterwick, Lavelle, Wassi, Harris, Torres (sub Tanner 70 mins), Preston, Joel (sub Scott 76 mins), Doyle.
Subs not used: Stanford, Wall.