Spence arrived on a free transfer from Crystal Palace over the summer and his first league goal for the Blues was one to remember.
Gary Holt provided the assist for the 20-year-old, who fiercely drove the ball into the bottom right corner of the goal from the edge of the box on 34 minutes.
Man-of-the-match Spence, who made his debut for Palace under now Wycombe boss Peter Taylor, left Barry Roche in the Morecambe goal with no chance of making a save and launched the Chairboys season in style.
The Shrimps, who are now in their second season in the Football League, hit back after 66 minutes however through David Artell, who poked home a Jim Bentley knockdown.
And the away side almost took the lead four minutes later as Michael Carr had a shot cleared off the line by Craig Woodman.
Wycombe had a number of good chances in the second half to regain their lead with both Gavin Grant and Spence forcing good saves from Roche, but the side who finished seventh last year in League Two couldn't find the winning goal.
Torrential rain caused both sides problems from the first whistle as the ball skidded from end to end, but it was Wycombe who had the slight edge throughout the 90 minutes and will feel the most disappointed with the draw.
Their next challenge is a tough visit from Championship side Birmingham City on Wednesday in the League Cup, and they will be hoping that Holt, who went off with a thigh strain at half-time, makes a full recovery.