The Blues had trailed at half-time to a Darijan Matic strike in front of 16,000 inside the Stozice Stadium.
But the Spain team-mates combined for Chelsea’s equaliser after 55 minutes, before Kurt Zouma prodded in a rebound eight minutes later.
Boss Jose Mourinho said: “We feel we are going to be very strong and we want to fight for the title.”
The match also featured an terrible miss from Fernando Torres, who chested a Nathan Ake cross over the bar from two yards out, with the goal gaping.
New signing Didier Drogba, in his second spell at the club, did not feature, but watched on from the sidelines.
Chelsea first half: Delac, Azpilicueta, Zouma, Cahill, Luis, Fabregas, Matic, Salah, Boga, Brown, Costa.
Chelsea second half: Cech, Ivanovic, Zouma, Terry, Ake, Fabregas (Romeu 63), Matic (Solanke 70), Van Ginkel, Salah (Chalobah 70), Costa (Bamford 70), Torres.
Goals from Harry Kane and Aaron Lennon gave Tottenham a 2-0 friendly win over Chicago Fire in the United States.
Mauricio Pochettino’s side extended their unbeaten pre-season start to three matches as Kane scored in the fifth minute.
Lennon sealed the victory when he converted a Roberto Soldado through ball with six minutes to go.
“It was difficult in the humidity but well done to the players, it was a good game out there,” Pochettino said.
Tottenham had begun their tour of North America with a 3-3 draw against Seattle Sounders and a 3-2 victory over Toronto.
Tottenham: Friedel (McGee 78), Walker (Naughton 46), Dawson, Veljkovic (Fredericks 80), Rose (Davies 46), Capoue, Mason, Holtby (Falque 64), Lamela (Eriksen 46), Townsend (Lennon 46); Kane (Soldado 46).
Subs not used: Kaboul, Ceballos.
Real Madrid 1-1 Inter Milan (2-3 pens)
A stunning Gareth Bale goal was not enough to give Real Madrid victory in their pre-season International Champions Cup meeting with Inter Milan in Berkeley, California.
Wales international Bale surged through the Inter midfield before beating keeper Samir Handanovic with a powerful swerving 30-yard shot after 10 minutes.
But Argentine striker Mauro Icardi equalised with a penalty after a foul on Nemanja Vidic – before scoring the decisive kick as Inter won in a shootout.
“Gareth Bale is working well and has a great attitude,” said Real Madrid coach Carlo Ancelotti.
“He will improve and this will be a very different campaign for him, especially in terms of the start of the season, as he didn’t have a pre-season last year.”
AC Milan 1-5 Manchester City
Manchester City thrashed AC Milan 5-1 in a game suspended for 30 minutes because of a severe thunderstorm.
Stevan Jovetic, Scott Sinclair, Jesus Navas and Kelechi Iheanacho put City into a 4-0 lead within 26 minutes in Pittsburgh, USA.
Sulley Muntari pulled a goal back for Milan before half-time and the restart at the Heinz Field stadium was delayed because of bad weather.
Jovetic added a fifth, while Milan’s Mario Balotelli had a goal disallowed.
City now face Liverpool on 30 July.
Manchester City: Caballero, Clichy, Kolarov (Richards 69), Boyata (Rekik 77), Nastasic, Fernando (Garcia 62), Zuculini (Rodwell 77), Navas (Leigh 77), Jovetic (Guidetti 69), Iheanacho (Huws 62), Sinclair.
Olympiakos 0-1 Liverpool
Raheem Sterling scored the winner as Liverpool beat Greek side Olympiakos at Soldier Field in Chicago.
Sterling latched on to a deflected shot from striker Daniel Sturridge to score from close range early in the game, while the closest Olympiakos came to an equaliser was when a Gevorg Ghazaryan effort hit the crossbar.
Reds captain Steven Gerrard started alongside Sterling, Sturridge and summer signing Lazar Markovic, who joined the club from Benfica for £20m.
Winger Markovic played the first half before being replaced by Brazilian Philippe Coutinho.
“Markovic will only get better and better,” said Liverpool manager Brendan Rodgers.
“He showed great strength when he burst through and hopefully later on when he picks up that speed and sharpness in his game, he’ll go on and finish that.”
Liverpool: Jones, Johnson (Kelly 62), Skrtel, Toure (Coates 62), Enrique (Robinson 45), Gerrard (Leiva 62), Henderson, Can (Allen 45), Sterling (Ibe 75), Markovic (Coutinho 45), Sturridge (Lambert 74).
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Source: BBC Sport