The 22-year-old, who joined Wycombe in the close season after leaving Plymouth on a free, headed home a pin-point Dean Morgan cross inside the opening 10 minutes.
Morgan twice could have put the game beyond doubt after the break, but could not convert while Wycombe goalkeeper Matt Ingram was on hand to deny Jack Sampson in the second half.
Morecambe were 1-0 down after just seven minutes as Morgan wrong-footed Chris McCready before crossing for Cowan-Hall to put the Chairboys in front.
Josh Scowen and Jon-Paul Pittman were then wasteful for Wycombe, while McCready almost made amends for Wycombe’s opener, but his header after 36 minutes hit the crossbar.
Morgan dragged wide from 15 yards five minutes after the break and was then denied by Barry Roche with Morecambe striker Sampson firing wide just before.
The 20-year-old then had a golden chance to equalise, but he could not beat Ingram from close range as Wycombe held on for a 1-0 win.