Armstrong caught two passes - both for touchdowns - for 78 yards and scored on a 24-yard run. Blake Martin added 13 carries for 63 yards and a score.
Lawrence hit Armstrong for a 16-yard score on the final play of the first quarter and Martin's 21-yard touchdown with 52 seconds left in the second gave San Diego (4-2, 3-1 Pioneer League) a 14-0 lead at the half.
Armstrong scored on a 62-yard catch-and-run late in the third before his touchdown run capped the scoring with 3:24 to play.
Drake (3-4, 2-2) was limited to 61 yards rushing and was held scoreless for the second time this season.
San Diego posted its first shutout since a 59-0 win over Stetson on Sept. 28, 2013.