But the Cumbrians were pushed all the way and can count themselves fortunate, after the plucky Seagulls hit the woodwork and had what looked like a stonewall penalty turned down.
And the home side needed another slice of luck to take the lead against the run of play in the 35th minute.
Tricky winger Simon Hackney cut the ball back from the byline, only for the desperately unlucky Steve Thomson to slice the ball on to Graham's chin and past the prone Michels Kuipers.
Brighton had taken the game to Carlisle from the very first minute and should have taken the lead 60 seconds before Graham's intervention, after keeper Keiren Westwood had spilled David Martot's low angled drive.
The visitors' ex-Carlisle striker, Glenn Murray, was on hand to tuck in the rebound, but Westwood made up for his mistake with a stunning point-blank save to deflect the ball on to the bar.
Five minutes later Murray, a £300,000 January signing from Rochdale, was tripped in the penalty area by Peter Murphy but referee Mike Pike, himself a Cumbrian, waved away the furious Brighton protests.
Graham had earlier forced Kuipers into an excellent fingertip save but, in truth, Brighton were left kicking themselves for not being level at half-time.
And 13 minutes after the break their misery was complete as Carlisle secured the points and rap up their 13th successive home win.
Marc Bridge-Wilkinson's corner was only cleared to the far post, where Murphy was on hand to hook the ball back into the danger area, allowing Danny Livesey to smartly volley in from eight yards.