The growth of social-media platforms has been remarkable in terms of both number of users and volume of content generated. Twitter now reports approximately 166M daily active users who generate in excess of 500M tweets. Such volumes pose major challenges when it comes to providing analytics services and sentiment analyses for specific issues. As citizens tend to freely express their sentiments on social platforms, Twitter has inherently become an indispensable source for the public discourse in a wide variety of topics. Carrying out sentiment analysis on a timely manner on streamed tweets is undoubtedly a demanding endeavor. In this paper, we propose a Spark-based Twitter sentiment analysis software architecture that receives online streamed messages and compiles analytics. We outline the main elements of our proposal and discuss how they collectively help address the challenges involved in this big-data processing task. In particular, our framework: i) exploits the Spark machine-learning library to classify Greek tweets in a timely-manner, ii) manages streamed tweets in synergy with contemporary queuing and in-memory data systems, and iii) determines with high accuracy whether a sentiment is expressed by a genuine account. We report on the findings while experimenting with a novel model for sentiment analysis we created for Greek and ascertain the effectiveness of our proposed architecture.