A 10th-minute John Terry header ended Scarborough's FA Cup dream but the non-league side gave Chelsea a real scare.
Frank Lampard hit the post in the opening minute before Terry headed in after Mario Melchiot's flick-on.
Chelsea pushed for a second but Lampard spurned a series of chances and Leigh Walker saved a William Gallas header.
Colin Cryan had a header saved as Scarborough rallied and the home team were unlucky not to get a penalty when Gallas handled late in the match.
Scarborough struggled to match their illustrious opponents in the opening minutes of the fourth round tie but gradually found their rhythm.
Although Scarborough never really looked liked equalising for most of the match they rode their luck and can boast a scoreline few would have predicted.
Chelsea, on the other hand, stuttered after scoring early on and the expected flood of goals failed to materialise.
Boss Claudio Ranieri watched his team squander chance after chance and must be glad to have escaped from what turned out to be a very tricky tie.
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KEY MOMENTS
1 min: Lampard hits the woodwork
10 mins: Terry heads Chelsea in front
65 mins: Lampard misses with three attempts
80 mins: Cudicini saves Cryan's header
82 mins: Gallas appears to handle - but no penalty is given
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Lampard gave an early indication of Chelsea's intent with his thundering 40-yard drive that swerved viciously and crashed against Walker's goalpost.
And the Premiership side took the lead within 10 minutes.
A short-corner routine culminated in a Jimmy Floyd Hasselbaink cross that Melchiot headed across goal for Terry to convert from short range.
The Seadogs' problems increased when central defender Steve Baker was stretchered off and replaced by Steve Capper.
With the home team struggling to retain possession, Lampard went close again for Chelsea with another long-range strike.
Scarborough finally threatened after 19 minutes, Jimmy Kelly launching a powerful strike after neat approach work but his shot struck Terry and the chance was gone.
Chelsea should have scored again after 25 minutes but Jesper Gronkjaer shot tamely with only the goalkeeper to beat and Walker made a comfortable save.
But after a nervous opening with only Kelly's effort to show for their endeavour, Scarborough settled into the match and enjoyed a good 15-minuite spell towards half-time.
The home team started to press the Chelsea defence and Clint Marcelle was through on goal close to the break.
The former Stevenage Borough striker was flagged offside but replays suggested the decision was harsh.
Terry issued a timely reminder of the home team's quality on the stroke of half-time with a mazy 50-yard run into the Scarborough penalty, but the defender shot wide from 18 yards.
Hasselbaink shot inches wide from 35 yards seconds after the resumption of play.
Chelsea, with Emmanuel Petit on for Gronkjaer, controlled possession after the break but were guilty of over-playing in the opening 15 minutes.
Walker made an amazing save after 59 minutes, parrying Gallas' near-post header.
Lampard had three attempts from short range in the space of as many seconds, twice hitting a defender and then seeing his final effort saved as the Seadogs defiantly kept themselves in the tie.
Shortly afterwards Lampard shot over from 10 yards.
Chelsea's failure to take their opportunities was almost punished with a Boro equaliser.
Colin Cryan had a golden chance to score.
He met Chris Senior's flick-on unmarked, but his header was saved by Cudicini.
Shortly afterwards Gallas appeared to handle inside his own area, but Barry Knight refused the home team's penalty appeals, much to the disgust of the Boro fans.
Scarborough: Walker, Lyth, Cryan, Hotte, Baker (Capper 13),
Sestanovich, Kerr, Kelly, Marcelle, Quayle, Whitman (Senior 72). Subs not used: Williams, Glen Downey, Sollitt.
Booked: Hotte.
Chelsea: Cudicini, Melchiot, Gallas, Terry, Bridge, Cole,
Lampard, Nicolas (Oliveira 67), Gronkjaer (Petit 45),
Gudjohnsen, Hasselbaink.
Subs not used: Sullivan, Johnson, Huth.
Booked: Terry, Melchiot.
Attendance: 5,379.
Referee: B Knight (Kent).