The Merseyside outfit could have gone five points clear of Stevenage, who occupy 21st position, but a goal in each half from Adebayo Akinfenwa proved decisive for the visitors.
Tranmere's position was not helped by a straight red card for full-back Jim McNulty with Gillingham leading 1-0.
Ryan Lowe halved the deficit for Ronnie Moore's men in the 77th minute, but Tranmere were condemned to a second consecutive league defeat.
In League Two, Paul Cook's Chesterfield moved to the summit with a 2-0 triumph at Exeter City.
Oliver Banks broke the deadlock in the 48th minute, much to the delight of the travelling fans.
And the result was put beyond all doubt with 20 minutes remaining as forward Marc Richards doubled Chesterfield advantage.
Elsewhere, Southend United missed the opportunity to go third as they were held to a 1-1 draw by fellow promotion-hopefuls Rochdale at Roots Hall.
Jamie Allen put Rochdale ahead in just the 14th minute, but Kevan Hurst scored on the stroke of half-time to ensure a share of the spoils for Phil Brown's side.
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