Cepelova had won the only previous meeting between the two, in Montréal six months ago, and caused the No.2 seed a few anxious moments, particularly in the second set.
After taking the opener with a solitary break and moving 2-0 up in the second, Arvidsson's hitherto flawless serve started to let her down, with a couple of untimely double faults allowing Cepelova to break twice in quick succession.
Luckily for the Swede, she followed up each of these games with a break of her own. The second of these proved decisive, and after one hour and 17 minutes on court she finally booked her second round berth.
"You know first match is always special, and I lost to her last time," Arvidsson said."I knew it was going to be a tough match and I'm so happy I could win."
For Arvidsson, who also won the title in 2006, the 64 64 victory was her 21st in Memphis, and with the tournament moving to Rio de Janeiro in 2014 she is desperate to make her final visit a memorable one.
"Of course is it always special walking on the court," she added. "Being defending champion is special. I love this place. It is the last year of the event so I am trying to enjoy myself.I want to win as many matches as possible."
Also advancing were Kirsten Flipkens and Kristina Mladenovic. Top seed Flipkens continued her promising early season form by swatting aside Shahar Peer, 62 62, while Mladenovic was equally impressive in seeing off American wildcard Courtney Collins, 63 61.
Meeting Mladenovic in the second round will be another wildcard, Victoria Duval, who defeated Johanna Larsson, 36 61 63, for her first WTA main draw win.
"It was definitely really hard today," Duval said. "She is a Top 60 player so I went out there with no pressure, but I'm glad I pulled through.
"It's a great opportunity this week. I remember three years ago they gave me the wildcard in qualifying so to come back and get the wildcard in the main draw and get through the first round is great. Hopefully, I'll do even better tomorrow."