The second set remained tight, with the British No 1 breaking to take a two-set advantage - finished off with a thumping forehand into the corner.
The Mallorcan Munar trailed 4-0 in the third, and despite being broken, Edmund held his nerve to seal his progress to a second-round date with 2014 quarter-finalist Fernando Verdasco.
Heather Watson defeated Caty McNally
Image credit: Eurosport
Heather Watson made a winning start to her Wimbledon campaign with a 7-6 (3) 6-2 win over American world number 165 Caty McNally in the first round on Court 12.
In her 10th straight appearance at the All England club, British number two Watson saved two set points in the first set, but came through the tie-break 7-3 and dominated the second set 6-2 to set up a meeting with Shelby Rogers or Anett Kontaveit in the second round.
Watson's Grand Slam best is reaching the third round three times at Wimbledon in 2012, 2015 and 2017, and the Australian Open third round in 2013.
Watson hit 12 winners compared to 22 by 17-year-old McNally, but threw in 38 unforced errors compared to Watson's 19 in a contest lasting 102 minutes.