Rochdale moved into the play-off places after they saw off fellow promotion chasers Southampton.
Joe Thompson put the home side ahead when he headed in a Nicky Adams cross at the far post.
O'Grady doubled the lead just before the break when he collected a Matt Done pass and drove in.
Dale goalkeeper Owain fon Williams was in fine form to keep out Rahdi Jaidi and substitute Adam Lallana, who also saw a shot hit the post.
Southampton boss Nigel Adkins told BBC Radio Solent:
"We're obviously disappointed with the two goals because they are goals we should be stopping.
"The positives are the attitude of the players. They responded in the second half and created numerous opportunities, but you have to put the ball in the back of the net.
"We'll analyse this game, draw a line underneath it and then we'll move on having learnt the lessons."