After coming through three qualifying matches, Holmgren started the main tournament with a three-set win over Frenchman Quentin Halys, who is ranked 46th in the world.
Holmgren, who is ranked 192 in the world, won 7-6, 6-3, 6-4.
The Dane is known for having a powerful serve, and on Wimbledon's humble court 6, the serve worked even better than normal.
Time and time again, Halys looked visibly deflated when Holmgren hammered a serve down the line, dusting up the chalk from the grass.
Holmgren produced 20 aces, and Halys only managed to get barely half of Holmgren's first serves into play.
Holmgren lost just a single point in his first five service games in a first set, which Holmgren won in a tiebreaker, 7-4.
In the second set, both players enjoyed more chances for service breakthroughs. Holmgren was the first to strike, when he took advantage of two French double faults to take a 4-2 lead.
However, Holmgren struggled a bit to serve the second set home as he needed four set points to finally claim the second set.
Halys had a bad start to the third set. The Frenchman made three unforced errors to help Holmgren to an early break.
Now it looked really bleak for Halys, who needed his first serve breakthrough to survive in the match.
But Holmgren continued to serve unaffected, even though he was approaching the biggeest result of his career.
Halys is also known for his strong serve, and it also proved valuable against Holmgren. The only difference was that Holmgren was just a notch better at the decisive moments.
Thus, Holmgren converted two out of four break points, while Halys missed his four.
The Dane took advantage of the first match point and can now look forward to a second round tie against 21st-seeded Czech Tomás Machac.