Goals from Diego Costa and Ruben Loftus-Cheek sealed the victory for interim coach Guus Hiddink, as the Blues cantered into the next round of the competition.
It was a steady day's work for the Premier League champions, who played well within their capabilities for the duration of the match, rarely having to find top gear.
Hiddink fielded a strong team for the tie, playing a formidable starting XI as Pedro replaced the injured Eden Hazard. Scunthorpe boss Mark Robins made one change to his team following their draw with Wigan last weekend, as new signing Murray Wallace started ahead of Niall Canavan in defence.
ESPN FC's Liam Twomey commented on the vocal support of the travelling fanbase:
Scunthorpe United fans in fine voice in the Shed End. They've clearly travelled to London with Bradford City-level optimism #cfc— Liam Twomey (@liam_twomey) January 10, 2016
The north Lincolnshire side sat deep from the opening stages, allowing Chelsea to have the ball in midfield as the Blues pushed forward.
The hosts soon took the lead as their early pressure paid off, with Costa claiming the opening goal. Branislav Ivanovic's right-wing cross was measured to perfection, and the Spain international attacked the penalty box, adjusting his body to deflect the ball into the net.
Twomey called the action as Costa continued to improve his recent record:
Chants of 'Diego' as Costa scores his fourth goal in three games from an Ivanovic cross. Once again the darling of Stamford Bridge #cfc— Liam Twomey (@liam_twomey) January 10, 2016
Despite taking an advantage in the tie, journalist Piers Morgan was frank about Chelsea's ambitions for their season ahead after a disastrous run:
Chelsea are underdogs today & this is their only chance of a trophy. https://t.co/wFSu765rse— Piers Morgan (@piersmorgan) January 10, 2016
Costa was certainly in the mood for action, looking like a different player from the one who featured under Jose Mourinho. The striker was powerful through the middle, giving Cesc Fabregas and Willian a viable target.
However, the Blues lost impetus in the closing stages of the half, as Scunthorpe ventured forward. The Iron had a couple of half-chances before the referee's half-time whistle, but they could not capitalise.
The Premier League champions were once again patient in their approach in the second half, with the home support quiet as they waited for their team to produce some excitement.
However, it was Scunthorpe who seemed motivated to get their name on the scoresheet, as an edgy feeling passed over Stamford Bridge.
BT Sport's Owen Hargreaves (h/t the club's official Twitter account) commented on Scunthorpe's increased threat:
HARGREAVES: "That was good from Scunthorpe. They're getting more bodies forward and looking much more positive."— Scunthorpe United FC (@SUFCOfficial) January 10, 2016
The visitors had a huge shout for a penalty turned down as Kevin van Veen was toppled by Ramires in the box, but just as Scunthorpe looked good for an equaliser, the Blues extended their lead against the run of play.
Loftus-Cheek claimed the goal with a clinical left-foot finish.
Opta Joe highlighted a milestone for the highly rated midfield talent:
1 - Ruben Loftus-Cheek scored with his first ever shot on target for Chelsea, in what is his 11th appearance for the Blues. Prospect.— OptaJoe (@OptaJoe) January 10, 2016
The atmosphere collapsed after the second Chelsea strike, as Scunthorpe's charge appeared to have derailed. The hosts set about playing keep-ball for the closing 15 minutes, clearly content with their day's work.
There was a late scare for the hosts as Jordan Clarke rattled his shot against the woodwork, but the moment was the visitors' highlight of the match.
It was a professional day at the office for Chelsea, as they strolled to the final whistle, placing them into the hat for the next round of the FA Cup.
Hiddink lauded the talent of Loftus-Cheek after the game, saying he believes the player is mature beyond his teenage years, per BT Sport:
Robins said he thought his team gave Chelsea too much respect on Sunday, but was proud of the way his side developed in the second half, per BT Sport:
The draw for the fourth round of the FA Cup takes place on Monday evening, live on BBC One at 7:15 p.m. GMT.