Andros Townsend gave the hosts the lead at the end of a strong spell but a brace from Beattie either side of a scruffy goal from Joe Allen proved enough to inflict an eighth defeat in 10 league games on Keane's side.
Town had lost their last four league games, culminating in a humiliating 4-1 derby defeat at Norwich last Sunday, but responded to record a midweek win over West Brom which booked their place in the semi-finals of the Carling Cup.
But league form is what matters most to Ipswich fans and Keane remains firmly under pressure after more woeful defending allowed Brendan Rodgers' men to escape with the win.
The victory, coming after last Friday`s home loss to Portsmouth, maintains Swansea`s record of having bounced back to win immediately after each one of their six league defeats so far this term - a true sign of real promotion contenders.
Source: PA
Source: PA