The two teams largely cancelled each other out in an intriguing clash, with clear-cut chances limited throughout.
Although Rochdale had the better of the game, it was home keeper Frank Fielding who produced the best two saves, one late in the first half to prevent an own goal and another in the second half to deny Stuart Lewis.
The closest Rochdale came was through two substitutes, as Joe Thompson blazed wide from an angle and Chris Dagnall was well denied by Simon Royce at the near post.
Royce also saved well from Gary Jones' piledriver but the two sides start on an even keel in Sunday evening's second leg.
Both teams were much changed from Saturday's prequel to the semi-final, which was won 1-0 by the Gills.
The first chance fell to the home side in the sixth minute when Adam Rundle made space on the edge of the box and fired a shot which was deflected over the top.
Chances were at a premium but Rochdale were inches away from an opener when Will Buckley fizzed a low shot just past the post.
Buckley did have the ball in the net seven minutes before the break, but his celebrations - and the obligatory post-goal music - were cut short by an offside flag.
But the Gills almost grabbed a half-time lead when Simeon Jackson crossed from the right towards Andy Barcham and Fielding had to scramble to his right to stop an own goal, and then did well to catch Barcham's attempted chip back across goal.
Buckley fired high and wide early in the second half, before Jones forced a save out of Royce, but the veteran Gills stopper was up to the challenge of his 30-yard effort.
Barcham went on a fine run on the hour but his shot was blocked out for a corner long before it might have troubled Fielding.
Substitute Thompson broke into the box in the 66th minute but his powerful shot from a narrow angle thumped into the crowd behind the goal, before John Nutter gave Royce a scare with a header which had a bit too much pace on it, but Royce clung on.
Nutter soon caused panic at the other end as well, his low cross finding Barcham, whose shot was almost blocked into Mark McCammon's path, and the resulting corner from Josh Wright almost curled straight in.
Lewis let fly with an opportunist strike from 25 yards which forced a fine save from Fielding as the Gills enjoyed their best spell of the game.
Dagnall was played in by Thompson but Royce saved well at the near post, only for referee Kevin Friend to give a goal kick.
Ten minutes from time they were awarded a corner, but Royce saved well, before Dagnall had time and space to let fly from 25 yards, but was wide of the target.
And four minutes of stoppage time was unable to bring a winner to leave the Gills slight favourites ahead of the return leg.