The summer signing scored twice in the first seven minutes to secure the win for Jose Mourinho's side.
Read how all the action unfolded below:
7.16pmGood evening! It's just half an hour until the final match of Chelsea's pre-season schedule gets underway at Stamford Bridge. Let's start with a look at the team news...
7.17pmCHELSEA STARTING XI: Courtois, Ivanovic, Cahill, Terry, Ake, Fabregas, Matic, Ramires, Hazard, Schurrle, Costa
7.18pmREAL SOCIEDAD STARTING XI: Zubikarai, Zaldua, Ansotegi, Martinez, De La Bella, Markel, Pardo, Granero, Prieto, Canales, Agirretxe
7.20pmCHELSEA SUBSTITUTES: Cech, Schwarzer, Azpilicueta, Christensen, Luis, Zouma, Mikel, Oscar, Van Ginkel, Salah, Moses, Willian, Torres
7.21pmREAL SOCIEDAD SUBSTITUTES: Rulli, Bardaji, Martinez, Estrada, Mikel, Elustondo, Yuri, Oyarzun, Hervias, Chory, Hernandez
7.24pmInterestingly, it's Thibaut Courtois who gets the nod ahead of Petr Cech in goal for Chelsea. The two keepers have been vying for the number one spot during pre-season, and with this being the final match before the start of the Premier League season, this could be an indicator that the young Belgian is Mourinho's preferred choice. There's no place in the squad for Didier Drogba though, he misses out after injuring his ankle during the win over Ferencvaros at the weekend.
7.27pmAhead of kickoff, the home side have been introducing their entire squad to the Stamford Bridge crowd. Despite his injury, Drogba did tkae take to the pitch, although it does look like he was limping somewhat.
7.30pmThe inclusion of Nathan Ake in the starting XI is also an interesting one. The youngster has been impressive in pre-season featuring regularly for the London side, often for more than 45 minutes. He did give away a penalty against Werder Bremen earlier this month, but will be hoping that he's done enough to earn a regular place in the first team this season.
7.34pmThis will be Sociedad's third match in Britain in the last week. They secures a 3-2 win over Aberdeen in a Europea League qualifier last Thursday, but lost 1-0 to Newcastle United a the weekend.
7.37pmThe Spanish side have been in reasonable form in the last month, winning three of their six outings, and drawing once in a friendly with Feyenoord.
7.40pmChelsea are being pretty active on Vine this evening. Here's an interesting look at Diego Costa's spot in the dressing room as he prepares for his first appearance at Stamford Bridge.
7.43pmPREDICTION! With just a couple of minutes until kickoff, there's just time to make a quick prediction. Real Sociedad should provide a tough test, but Chelsea's squad is strong enough to get the win. I think it'll be a 3-1 win for the home side.
7.45pmHere come the players! Both sides make their way out in front of a busy but not quite full Stamford Bridge.
1 minKICKOFF! Chelsea get the match underway.
2 minGOAL! Chelsea 1-0 Real Sociedad (Diego Costa)
2 minWell that didn't take long! After a couple of passes at the back, Diego Costa charges forward from midfield before rifling the ball in from the edge of the box. What a way for the Spaniard to mark his first home appearance for Chelsea.
3 minCHANCE! It should be 2-0 to Chelsea as Branislav Ivanovic makes a superb run forward before pulling the ball back to Ramires, who only had to slot the ball into an empty net, but somehow he managed to fire it over. The visitors are being completely outplayed at the minute.
5 minThe home side's relentless start continues as Fabregas wins a free kick from a dangerous position around 25 yards out. Andre Schurrle curls the ball into the box, but the Spanish side do enough to clear the danger.
7 minGOAL! Chelsea 2-0 Real Sociedad (Diego Costa)
7 minSchurrle collects the ball on the edge of the box and curls it towards the goal, only to see if effort kept out by the post. However, Costa is waiting and quickly pounces on the rebound to head in his second of the evening.
9 minThere's an injury concern for the visitors as Ion Ansotegi has to make his way to the sidelines for treatment. It's not clear what happened but it looks like he'll be alright to continue.
11 minThibaut Courtois gets his first meaningful touch of the night as he comfortably claims the ball from a Prieto cross. Sociedad are starting to see a little more of the ball now though so he'll have to stat alert.
12 minSUB! Well it looks like Ion Ansotegi's injury was worse than it first seemed as Mikel Gonzelez has taken his place for the La Liga side.
15 minBoth side's seemed to have settled down after the frantic opening 10 minutes. Chelsea are settling down into a steady rhythm just looking to keep the ball, while Sociedad are looking more organised at the back, and showing a bit more of a spark while going forward.
18 minCourtois comes for a Pardo cross, but really hasn't had a great deal to do so far. With Mourinho presumably preparing to make a host of changes at half time, the Belgian might have been hoping to show off with a few more saves before he's taken off.
20 minCHANCE! Real Sociedad have their first decent chance of the game as Esteban Granero unleashes a curling effort from just outside the box, but it swerved away from the post at the last minute.
22 minCosta has a chance to go for his hat-trick, but he selflessly passes to Cesc Fabregas instead, but the former Barcelona man's effort is blocked.
23 minFabregas appears to be through again for another attempt following a flick on from Schurrle, but the assistant referee flags the Spaniard offside.
25 minCHANCE! After Courtois claims another cross at the other end, Ake makes a blistering run towards the Sociedad goal before pulling the ball back for Costa. The new signing tries to fire in his hat-trick, but his shot lacks power and goes straight to Zubikarai.
28 minSociedad have been enjoying a decent spell of possession in the last couple of minute,s but lose the ball when Prieto wrong-foots Agirrexte with a pass out wide.
30 minCHANCE! Thibaut Courtois has made his first save of the game. It was very comfortably for the keeper as Granero failed to get a decent contact with his head, but Courtois was ready to deal with it anyway.
33 minFabregas looks for Schurrle with a long ball forward. Sociedad block the pass but it comes to Costa, who is fouled just outside the box to give the home side a free kick from a strong position. Fabregas and Hazard both look keen to take it.
34 minCHANCE! It's Hazard who takes it, and he curls it around the wall, but Zubikarai punches it clear.
36 minCHANCE! Mikel Gonzalez unleashes a rather ambitious effort from around 30 yards out, but Courtois watches it all the way and makes the save, although it looks like it may have been heading just wide.
39 minChelsea have yet another free kick in a dangerous area, and this time it's Schurrle who curls it in to his teammates in the box. Terry gets his head to it first, but he's being closely marked and slices his effort away from the goal.
42 minCHANCE! Costa continues to hunt for his hat-trick as Fabregas launches a long through-ball for the striker, but it has just a little too much pace, and Zubikarai collects it before Costa can unleash his strike.
45 minSociedad are trying to keep the ball as half time approaches, but Filipe Luis gets it back for the hosts and tries to launch Ake on a quick counter-attack.
45+1 minHALF TIME: Chelsea 2-0 Real Sociedad
8.33pmSo two goals in the opening seven minutes have given Chelsea a 2-0 lead over Real Sociedad at half time in their final pre-season friendly.
8.37pmEven after the initial flurry of activity settled down, Chelsea still created the majority of the chances and could easily have increased their lead, they have totally dominated the match so far.
8.41pmThibaut Courtois stopped a couple a off-target efforts and claimed a few decent crosses from the visitors, but really didn't have to prevent any real goal-scoring opportunities. With Petr Cech and Mark Schwarzer both on the bench, it seems likely that there will be a change in goal at some point in the second half.
8.47pmThe players are back out for the second half. It looks like there are quite a few changes, which we'll let you know about as soon as we have the lineups confirmed.
46 minKICKOFF! Real Sociedad get the second half underway.
47 minFilipe Luis has made a bright start to the second half, having replaced Ake at the break. He's already put in a couple of crosses for the hosts and won a corner.
48 minSUBS! There were four changes for the hosts before the start of the second half, with Azpilicueta replacing Cahill, Luis coming on for Ake, Willian replacing Ramires and Schurrle making way for Oscar.
51 minWillian is looking to make an impact early in the second half as he gets forward an puts the ball in for Fabregas, but Sociedad are doing just enough at the back to prevent the hosts from adding to their first-half lead so far.
54 minAgirrexte gets himself to space on the edge of the Chelsea box as he looks to hit the ball on the turn, but Terry and Azpilicueta do enough to get the ball clear.
55 minChelsea immediately head down the other end as they look to put the visitors back under pressure, with Costa getting the final touch, but his finish went harmlessly behind.
57 minChelsea are continuing to press, resulting in a shot for Eden Hazard, but he scuffs his effort and it fails to trouble the keeper.
59 minSUB! The visitors make another change, taking off Joseba Zaldua for Carlos Martinez.
61 minSUB! There will be no hat-trick on his home debut for Diego Costa, he's being replaced by Fernando Torres.
63 minWillian spots a gap and plays his way into the box with some flashy footwork, but Torres can't get on the ball for his first shot of the night.
65 minPENALTY APPEAL! Cesc Fabregas wins a corner for Chelsea as Gonzalez turns his effort behind, but the midfielder claims that he used his hand. However, the referee is not interested and awards the corner, but is fired well wide by Torres.
68 minHazard rounds a couple of defender before flicking the ball forward towards Willian, but Bergara does just enough to head the ball away. It feels like a third Chelsea goal is imminent, but Sociedad are defending well to frustrate their hosts.
70 minAzpilicueta bursts forward before sending in a brilliant cross from near the corner flag, but Zubikarai punches it clear before it reaches the waiting Torres and Hazard in the box.
72 minSUB! Mourinho is making another change, replacing Cesc Fabregas with John Obi Mikel. The Spaniard gets a huge cheer from the crowd as he makes his way off, he's put in a big effort this evening, and was involved in the build up to both of the goals.
74 minCHANCE! Torres is just a couple of inches away from extendind the home side's lead as he squeezes himself in between two defenders to meet a cross from Luis, but his header if a fraction too high.
77 minCHANCE! Sociedad have started to see a bit more of the ball again in the last couple of minutes and actually managed to test Courtois when Agirretxe tried the drill the ball in low from the edge of the box, but the shot was comfortably saved by the keeper.
80 minThe visitors are definitely looking more dangerous, but Ivanovic manages to beat Prieto to the ball to clear the threat.
82 minSUBS! There's a triple change for the home side as Kurt Zouma, Mohamed Salah and Marco Van Ginkel replace Ivanovic, Matic and Hazard.
85 minChelea are just looking to keep the ball a the moment. There'll be disappointed not to have added to their advantage in the second half, but will be pleased not to have let Sociedad back into the match in the last few minutes.
87 minSUB! There's an early exit for John Terry, as Andreas Christensen comes on for the last few minutes.
89 minVan Ginkel and Willian link up as the home side charge towards the Sociedad goal before Oscar unleashes a powerful strike in a crowded penalty area, but his finish bobbles just wide.
90 minOscar curls the ball in from a corner, which almost falls to Zouma for a close-range header, but Zubikarai just manages to snatch it away in time.
90+1 minFULL TIME: Chelsea 2-0 Real Sociedad
9.35pmSo the early brace from Diego Costa proved enough for Chelsea to seal the win. Real Sociedad's chances were few and far between, giving the home side a comfortable night's work at Stamford Bridge.
9.38pmThe home side certainly could have scored more goals this evening, but some good saves from Enaut Zubikarai and some poor finishing allowed the visitors to keep the scoreline respectable.
9.40pmWell that's it from Stamford Bridge this evening, but stick around to read our match report and join us again on Monday when Chelsea will begin their Premier League season against top flight newcomers Burnley. Thanks for joining me this evening, goodbye.