The visitors tried to find an instant response and almost got back on terms when Ricky Holmes's shot was kept out by Lillis.
However, Rochdale started to dominate proceedings and could have added to their lead when Lund's effort was heading for the top corner, only for Carson's flying save to frustrate the midfielder.
Dale continued to press as the interval approached, with Lund and Peter Vicenti going close to scoring a second.
In the end, the Lancastrians weren't made to pay for their missed chances as they went 2-0 up, with Ian Henderson latching on to a long clearance from Lillis before rifling a shot beyond Carson from the edge of the penalty area.
With just over an hour played, Rochdale made sure of the points when Vicenti's header, from Matt Done's cross, found the back of the net.
Portsmouth had little in response, with another N'Gala effort as close as they got to getting back into the game as Dale held on to their advantage.