The 156th-ranked qualifier showed remarkable skills to down second seed Lopez 6-4 6-4, causing the biggest upset in the singles draw.
The 25-year-old next faces another Spaniard and fifth seed Guillermo Garcia Lopez in the quarterfinals.
Bedene, who reached a career high of 71 last year, has a reputation of humbling higher-ranked opponents. The Slovenian residing in London had stunned then world no. 17 Stanislas Wawrinka in the 2013 edition of the tournament here before losing to the Swiss number two the following year.
After winning his dream match, Bedene said "I have won my second match here at the Centre Court. I am happy to have served well through the match and hope to maintain the same flow in the next match."
Lopez was gracious in his defeat.
"He (Bedene) played a great match, he was a better player than me in this match. I know it is always tough to play the first match of the season because you are not confident, need to adjust. Maybe I was a bit tired. I need to practice and get ready for the Australian Open. There are a lot of things I need to improve upon," said the 33-year-old.
Unseeded Pablo Carreno Busta of Spain lost his pre-quarterfinal to world number 38 Yen Hsun Lu 4-6 4-6 in 73 minutes.
Sixth seed Lu from Chinese Taipei will take on Agut in the quarterfinals. Top seed and defending champion Wawrinka, eighth seed Gilles Muller and fourth seed David Goffin already advanced to the quarterfinals from the top half.
Garcia Lopez, the fifth seed, also progressed to the quarterfinals with a 6-7 (1) 6-2 6-0 over Japanese number two Ito Tatsuma.
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