The goalkeeper arrived from Stoke City this summer knowing he had been brought in to provide back-up to Thibaut Courtois following the departure of Petr Cech.
While the Bosnian talked positively about challenging for a starting spot, Courtois’ quality meant Begovic’s best hope of competitive action lay in the Capital One Cup and perhaps a dead rubber at the end of the Champions League group stage.
A rush of blood from Courtois, however, earned the Belgian a 52nd-minute red card after his foul on Bafe Gomis conceded a penalty and provided Begovic with an unexpected chance to make his competitive debut on the opening day.
Begovic was on familiar territory, having made his Stoke debut on the same ground as a first-half replacement for the injured Thomas Sorensen during the early stages of a humiliating 7-0 defeat.
Saturday’s outcome was nowhere near as painful, but nevertheless felt like a blow to a side who have grown used to steamrollering visitors to west London, and it prompted a frustrated reaction from Jose Mourinho and his players.
Centre-back Gary Cahill described the outcome as two points lost and Mourinho took it out on his medical staff, criticising them for going onto the pitch to treat Eden Hazard for a minor injury, forcing the forward to leave the field of play in the final moments of the game when Chelsea were already under-manned.
The challenge is now to regroup ahead of a trip to the Etihad Stadium next Sunday when Begovic will again get his chance.
The keeper said: “It was a bit eventful. Not something you expect to happen that way. It was a very unfortunate incident. I feel a bit sorry for Thibaut.
“I haven’t seen a replay of the incident but it looked as though there were people covering for him and was a bit harsh. But I’m pleased to have made my debut.
“My Stoke debut came at Stamford Bridge in that kind of manner so it seems to happen here. It’s just one of things where you get thrown in and you have to be ready. But it went okay and we were a bit unlucky not to get three points.
“It’s the next stage of my career to be involved in these games. First and foremost, I came here to compete and be part of this great club and contribute to the team. And hopefully I do that over the next few weeks.”
Chelsea’s inability to start the season with a victory threw fresh focus on Mourinho’s failure to strengthen his squad significantly during the summer.
The home side twice took the lead, initially through Oscar in the 23rd minute and then again via a deflection off Swansea defender Federio Fernandez a minute after Andre Ayew’s 29th minute equaliser.
Courtois’ error, though, allowed Gomis to secure a point from the penalty spot and after a frantic final 38 minutes, both teams had cause for satisfaction and regret.
At least Mourinho can be assured he has cover of sufficient quality to replace Courtois, insisting the club had no reason to regret the absence of Cech.
“We don’t miss Petr,” said the manager. “We’ve got a good keeper. The problem with Petr is not that we miss him because we have two excellent keepers. The problem with Petr is that an opponent is better than before.
“Thibaut and Asmir are two fantastic keepers. My club did very well by getting a keeper on time and not on the August 31 because if my club gives me a keeper on August 31 then we have a problem not just for today but also for the next match.
Swansea’s performance confirmed their progress of last season when they finished an impressive eighth and was lit up by outstanding performances from Jefferson Montero and Jonjo Shelvey.
Shelvey, 23, was the subject of public criticism from his manager Garry Monk last season, who warned the player about his attitude and has clearly responded well.
“We got his father in and his agent in and we all had a good chat,” said Monk.
“We want the best for all the players at the club. That performance today will give him the confidence to push on a bit further.
“He went away for the summer and has come back with a good attitude and hopefully we will see an even better Jonjo. He realises how serious it is at this level and what type of player he can be, it’s all right me wanting it for him but he has to want it for himself.”
Courtois 4; Ivanovic 3, Cahill 7, Terry 6, Azpilicueta 7; Matic 6, Fabregas 5 (Zouma 76, 6); Willian 6 (Falcao 84, 6), Oscar 8 (Begovic 54, 7), Hazard 6; Costa 7.
Fabianski 6; Naughton 7, Fernandez 7, Williams 7, Taylor 7; Shelvey 8, Ki 6 (Cork 41, 7); Ayew 8, Sigurdsson 7, Montero 9 (Routledge 71, 6); Gomis 6 (Eder 79, 6).
Michael Oliver 7