Keith Hill and his counterpart Mark Stimson fielded weakened teams in preparation for the double-header to come with an appearance at Wembley the prize on offer.
The visitors looked threatening on the break throughout the first half and had an effort chalked off just two minutes in when Nicky Southall was judged offside.
Gillingham opened the scoring in the 20th minute when a poor free-kick from Mark Jones was headed out by Stuart Lewis to Weston and he ran from deep inside his own half into the Rochdale penalty area.
Weston managed to stay on his feet when Rory McArdle challenged from behind, bundling the ball past goalkeeper Frank Fielding at the second attempt.
Rochdale's Will Buckley and Jon Shaw had efforts cleared off the line while Gary Jones' volley was deflected over the top by Garry Richards and Simon Ramsden's chip was pushed over the bar by Alan Julian.
League Two play-off semi-final fixtures: First legs: Shrewsbury v Bury, Rochdale v Gillingham (both Friday 7 May).
Second legs: Bury v Shrewsbury (Sunday 10 May, 12pm), Gillingham v Rochdale (Sunday, 10 May 6.30pm).