Simeon Jackson scored both goals to make it 20 for the season as the Gills triumphed in the semi-final second leg at Priestfield.
Jackson kept his cool to fire home a second-half penalty and it proved enough for the hosts, with the first leg at Spotland last week having finished goalless.
The Canadian had put the Gills ahead in the first half, but his goal was cancelled out by Chris Dagnall's strike just before the break.
But Rory McArdle brought down John Nutter and Jackson - who sent his last penalty over the bar at Wycombe last month - scored the goal to set up a Wembley clash with the Shrews, who beat Bury on penalties earlier in the day.
The Gills were sloppy in possession early on, but they did muster the first effort on goal when captain Barry Fuller, yet to score for the club, tried his luck from 35 yards - but it was over the top.
Dale had their first chance when Tom Kennedy crossed for Lee Thorpe, but he headed high over the top - and the Gills went ahead in the 13th minute.
Dennis Oli won the ball off Rory McArdle and despite the ball accidentally striking his hand, played in Andy Barcham on the left. He crossed low and Jackson stole in front of his marker to net at the near post.
The goal settled the nervy home side down, and Barcham almost got on the end of a Jackson flick, before a brilliant solo run from the former Tottenham man ended with his shot being blocked.
A Nutter cross was then flicked on by Oli to Barcham but he could not direct his header goalwards.
But Dale levelled against the run of play in the 37th minute when Fuller's clearance was charged down and fell to Dagnall, who cut inside Nutter before finishing left-footed.
Thorpe had the first chance of the second half, but his header from Adam Rundle's cross was tame and straight at Simon Royce.
The Gills were awarded a penalty just after the hour when Barcham cleverly flicked in Nutter and he was brought down by McArdle, and Jackson stepped up to send Frank Fielding the wrong way.
And it was nearly three when a Nutter free-kick reached Garry Richards at the back post, but his looping header hit the top of the bar and bounced behind.
Rochdale manager Keith Hill responded by throwing on strikers Adam Le Fondre and Jon Shaw, and their presence almost forced an error as Royce made a hash of a corner, but he recovered well to cling on at the second attempt.
Jackson then curiously ran for the corner when the home supporters were screaming for him to try and complete his hat-trick, before McArdle headed over from a Kennedy cross.
Fielding went forward for a corner, and Will Buckley fired a last-gasp shot wide, but the Gills booked their third Wembley appearance in 10 years.