The sixth seed became the first Dane to win a match at the All England Club since Kenneth Carlsen in 2004 when he completed victory in a clash that began on Tuesday morning but was suspended because of the weather.
Tuesday's first set was closely fought, with Loffhagen cheered on by a supportive home crowd and showing much more skilful play than his world ranking of 371 would suggest, having climbed from 981st at the end of 2022.
However, Rune's precision and accuracy secured him the first set on a tiebreak before the match was suspended.
After play resumed the next day on Court Three, the Dane saved three break points in the first game of the second set, broke Loffhagen in the next game and held serve to race into a 3-0 lead.
The Briton did get on the scoreboard and clawed some games back with the help of five aces, but Rune was too good, bringing up three set points with a backhand volley and converting straight away.
Loffhagen, who worked in a London pub on a break from the sport before rejoining the men's Tour last year, could not halt Rune's momentum in the third set, netting to surrender a break in the first game.
As the evening drew in, Loffhagen was broken once more and sent a backhand into the net to hand the match to Rune who will face Italy's Matteo Arnaldi or Spaniard Roberto Carballes Baena in the second round.
"It means a lot... it's cool to come back with good memories, (and I) hope to bring better memories than last year," Rune, who lost in the first round in 2022, said in an on-court interview.