The Blues had an opportunity to leapfrog the Swans up the standings and appeared on track to do so when Bertrand Traore converted Nemanja Matic's assist in the 39th minute of the contest.
However, Stoke did not yield against the defending Premier League Champions and scored a deserved equaliser in the 85th minute after Chelsea keeper Thibaut Courtois punched Xherdan Shaqiri's cross into the path of Mame Biram Diouf, who finished from close range.
Bojan Krkic had an opportunity to snatch all three points for the visitors late in stoppage time but was denied by a strong save by Courtois.
Chelsea rested a handful of players who regularly feature in their starting XI for the clash with the Potters. It appears as though interim manager Guus Hiddink has shifted the club's focus from the lacklustre Premier League campaign to their hopes of winning silverware in the Champions League and FA Cup.
Stoke continue to stay within touching distance of a Champions League spot, with the draw against the Blues taking them to within five points of fourth-placed Manchester City.
Good result at Stamford Bridge to keep this positive run of games! Great to see the team fighting until the end! pic.twitter.com/dJTTrxKbzG
— Marc Muniesa (@muniesa92) March 5, 2016
Great result for us and we thoroughly deserved it too! keeps our unbeaten run going and first point at the Bridge for a long time! #SCFC
— Jack Butland (@JackButland_One) March 5, 2016
Good team effort and another important point gained here at Stamford Bridge! #SCFCpic.twitter.com/sv5l2HBrlc
— Bojan Krkic (@BoKrkic) March 5, 2016
Chelsea interim boss Guus Hiddink was pleased with the performance of the players he promoted to the starting XI:
"Stoke play well and creatively and they pushed us back. The first goal we got after a sloppy start, it was a beautiful goal. We have rested one or two players but it's good to see the players who came in, especially the young ones, like Traore and Ruben Loftus-Cheek, do well.
Stoke boss Mark believed his side could have take all three points from Stamford Bridge:
"We're grateful to equalise but we deserved more from the game. It was an excellent away performance - we took the game to Chelsea. We're really pleased with the performance. Their goal came out of the blue, it was a great bit of individual skill. I felt we were a strong team and made things happen."
*Thanks to Opta
5-1 - In the three games that Bertrand Traore has scored in for Chelsea before today, the Blues have won 5-1. Repeat?
— OptaJoe (@OptaJoe) March 5, 2016