Medical devices and methods for accessing an anatomical space of the body and particularly for penetrating the epicardium to access pericardial space and the epicardial surface of the heart in a minimally invasive manner employing suction are disclosed. The distal end of a tubular access sleeve having a sleeve wall surrounding a sleeve access lumen and extending between a sleeve proximal end and a sleeve distal end having a plurality of suction ports arrayed around the sleeve access lumen distal end opening is applied against an outer tissue layer. Suction is applied through the plurality of suction ports to a plurality of portions of the outer tissue layer. A perforation instrument is introduced through the sleeve access lumen to perforate the outer tissue layer to form an access perforation into the anatomic space while the applied suction stabilizes the outer tissue layer, whereby further treatment drugs and devices can be introduced into the anatomic space.