Player/coach Hamish Imrie and his new-look side, who are third in the men's Premiership, were 1-0 ahead at Peffermill, but Clydesdale, who are sixth in the top division, failed to convert a penalty corner.
The students netted a second then had to defend a series of penalty corners before breaking out to claim three goals late on and seal the game.
Imrie said: "This was a really good performance, particularly in the second-half, but we had to defend well against a good Clydesdale team."
Premiership side Inverleith were level at 0-0 at the first break against a determined and hard-working National League side Strathclyde University who are third in their table.
But former Commonwealth Games player Derek Salmond netted to ease home nerves in the second quarter and Tom Barton followed with a second just after half-time.
James Stuart, making his return to the squad after injury, claimed a third in the final session following a penalty corner award.
Coach Chris Duncan said: "This was a job done for us against a team from a lower division which fought really hard."
Elsewhere, Grange, second in the Premiership, disposed of city rivals Watsonians, who are fifth in the top league, 5-1 at Fettes College with Fraser Heigh netting twice and teenager Murray Banks also scoring.
Player/coach Callum Milne said: "This was a much improved performance and we controlled much of the ball, particularly after they had a red card issued against one of their players."