The form and functions of political discourse have considerably taken a new orientation with the evolving ways of communication. Twitter is a platform that is increasingly preferred by the political elites for the purpose of gaining public acclaim and propagating political ideologies. The political discourse on Twitter requires a critical attention toward linguistic structures and strategies to uncover the relationship between language and social practices. For this purpose, tweets of two eminent Pakistani political figures are chosen for unmasking a variety of discourse strategies at work from the perspective of critical discourse analysis (CDA) through the socio-cognitive model of ideological square. The analysis uncovers the hidden ideological structures and strategies realized through a number of rhetorical moves in the selected tweets. The cognitive binary of positive self-presentation and negative other-presentation help achieving political domination and legitimization of political actions by controlling the public opinion. The underlying motives vary and are context bound such as the aims to topple a government or to restore public faith in the governance. This research is significant for political discourse analysts as well as the general public, as a means for analytical activism propagated by any CDA inquiry, and paves way for further research in the use of social media platforms for political purposes.