The lone tally came in the 27th minute, when Oscar curled a free kick into the top corner. But while the Blues dominated this fourth-round tie, they were unable to convert their many chances into a second goal.
It was a seventh straight victory in all competitions for Jose Mourinho's side, who showed no ill effects following the transfer of playmaker Juan Mata to Manchester United on Saturday. Instead, both Oscar and Eden Hazard excelled once again in their creative roles as the Blues created wave after wave of attacks in both halves.
Chelsea will play at Manchester City in the fifth round.
Mourinho, who was celebrating his 51st birthday, made five changes to the side that defeated Manchester United in the league last weekend. January signing Nemanja Matic made his first start, with veteran Frank Lampard coming into the holding midfield alongside him. Andre Schurrle replaced Willian in the attack, Ashley Cole started at left-back and Mark Schwarzer replaced Petr Cech in goal.
For Stoke, manager Mark Hughes made four changes to the team that lost at Crystal Palace. Asmir Begovic replaced Jack Butland in goal, and Wilson Palacios, Marko Arnautovic and Stephen Ireland slotted into the midfield.
Eto'o, who bagged a hat-trick in the win over United, came within inches of scoring the opener in the second minute. After receiving Hazard's pass with his back to goal, the Cameroonian striker held off two defenders, turned and rolled a shot narrowly wide of the far post.
Stoke responded at the other end, where Peter Crouch headed Jonathan Walters' cross off target in the fifth minute.
Chelsea had a penalty appeal in the 14th minute after Hazard went to ground while running past Palacios in the box. Referee Chris Foy waved play on, with replays suggesting any contact was minimal.
The Blues broke through in the 27th minute via a superb piece of individual skill by Oscar. After Eto'o won a free kick on the right, Oscar curled his shot over the wall and beyond Begovic's reach at the far post to give Chelsea a 1-0 lead.
It was nearly 2-0 in the 40th minute. Working to the byline down the right, Hazard pulled back for Lampard in the middle, but Lampard was unable to redirect the ball into the net from close range despite being unmarked. Stoke countered quickly, and moments later Ireland fired into the side netting from the left flank.
Chelsea came close again in the 41st minute, but Oscar's low shot bounced off the near post and away to safety. Lampard shot off target three minutes later as the hosts tried to add a second before half-time, but the Blues had to be content with a 1-0 half-time lead.
After the restart, Chelsea picked up where they left off, Schurrle hitting the woodwork with a high shot from the right in the 48th minute. Oscar curled an attempt wide in the 53rd minute, and Schurrle shot straight at Begovic two minutes later.
The second goal proved hard to find, though. Lampard came close with a well-struck volley from distance in the 76th minute, and Eto'o bundled a shot wide with the goal gaping one minute later following Hazard's excellent dribbling down the left.
Luiz came closer still in the 84th minute with a fiercely struck free kick from outside the box, but Begavic reacted just quickly enough to punch the ball away.
The teams remained separated by just the single goal until the final whistle, but despite the closeness of the scoreline, the match fizzled in the closing stages. In the end, Chelsea advanced comfortably
|Chelsea Player Grades vs. Stoke City|
|Ramires (for Schurrle, 70')||DM||N/A||6|
|Willian (for Oscar, 81')||Wing||N/A||7|
|Demba Ba (for Eto'o, 85')||ST||N/A||No rating|
Both teams return to the Premier League with midweek matches.