Gauff needed just 51 minutes to see off 33-year-old Rus as she booked a meeting with Ukraine's Dayana Yamstremska for Saturday.
The US Open champion lost just 18 points throughout the match – eight in the opener and 10 in the second set – as she put any doubts over her recent form to bed in emphatic fashion.
Gauff's power proved too much for Rus in the opener, the third seed winning 88 per cent of points behind her first serve and converting three of four break points to go a set up in just 23 minutes.
Rus brought up four break points midway through the second set, but when she failed to convert them, Gauff punished her in ruthless fashion by reeling off another three games then finishing things with a terrific forehand winner.
Speaking after her win, the American said: "I played really well today. It was just one of those days for me… 6-0 6-0, I've never done that before, I'll probably never do it again."
Data Debrief: Gauff matches Azarenka, Halep feat
Gauff is just the third player to register a 6-0 6-0 win in the women's singles draw at the Madrid Open, following in the footsteps of two former world number ones in Victoria Azarenka and Simona Halep.
The American, who only turned 20 last month, is also the youngest player to double bagel an opponent in any main-draw match on the WTA Tour since Iga Swiatek did so against Karolina Pliskova in the 2021 Italian Open final in Rome.
In her first professional match in almost half a year, world number two Halep, who skipped last week's Palermo Open and will not make a decision on whether to play the US Open or not until after the tournament in the Czech Republic, was made to work hard for victory by the unseeded Hercog.
The Romanian picked up an early break and responded to dropping her serve in game three of the first by reeling off the next four in succession to take the set.
When Halep started the second set by breaking Hercog the writing appeared to be on the wall, but the Slovenian world number 46 fought back valiantly to force a decider in emphatic fashion.
Halep was unable to convert any of the six match points that came her way after breaking for a 5-3 lead, with Hercog clinging on to take the match to a third-set tie-break.
After failing to consolidate an opening mini-break, Hercog's resistance was finally broken after two hours and five minutes when a forehand into the net sent top seed Halep into the second round.
Wildcard Barbora Krejcikova ensured Halep's next match would not be an all-Romanian affair by beating Patricia Maria Tig 6-4 6-3.
Second seed Petra Martic defeated Varvara Gracheva 7-6 (7-2) 6-3 and third seed Elise Mertens needed three sets to overcome Jasmine Paolini 7-5 4-6 6-3.
A number of other seeded players were not as successful. Ekaterina Alexandrova (5) fell to qualifier Lesia Tsurenko, while Anastasia Pavlyuchenkova (6) went down 7-5 6-2 to Arantxa Rus, and Anastasija Sevastova (9) lost 6-2 6-2 to Irina-Camelia Begu.
Ostapenko looked to be cruising after winning the opener, but Kanepi levelled in the second despite the Estonian watching five set points come and go.
Kanepi then romped to victory with a stunning final set to defeat Ostapenko 4-6 6-4 6-0 and keep her hopes of winning her home tournament alive.
In second-round action, Beatriz Haddad Maia is through to the quarter-finals after a 6-1 7-5 success over Linda Noskova.
After Haddad Maia cruised to a one-set lead, the second was a much tighter affair before the Brazilian's class showed as she broke Noskova and then held serve to earn a straight-sets win.
Second seed Belinda Bencic also secured her place in the final eight with a 6-4 6-7 (2-7) 6-3 triumph over Katie Boulter.
At the Parma Ladies Open, top seed Maria Sakkari came from behind to beat Arantxa Rus and seal her quarter-final spot.
Rus saved five out of five break points as she won the opening set 6-3 to give her hope of an upset.
Those hopes were soon dashed though as world number seven Sakkari broke twice to take the second set 6-2, before clinching the match in the third to tee up a clash with Maryna Zanevska.
World number 33 Irina-Camelia Begu made it 12 consecutive wins on clay by overcoming Matilde Paoletti in straight sets and will face fellow Romanian Ana Bogdan in the next round after she beat Anna Karolina Schmiedlova 6-2 3-6 6-3.
Fourth seed Sloane Stephens saw her tournament come to an end after she was defeated by Danka Kovinic.
It was an ominous start for Cirstea, being broken to love in the opening game, but she stuck with second seed Sabalenka and broke back, before ultimately being pipped to the first set by the impressive Belarusian.
The key was on break points, with Sabalenka claiming all five that she won against the Cirstea serve, while saving six of eight on her own as she ultimately eased to victory.
Sabalenka now has 26 wins on clay in the WTA since 2021, with only Ons Jabeur (37), Iga Swiatek (34), Paula Badosa (31) and Coco Gauff (28) having more during this time.
Gauff also advanced after a routine 6-4 6-1 win over Irene Burillo Escorihuela, making the sixth seed in Madrid the first player to win 35 WTA-1000 main draw matches as a teenager since 2009.
Ninth seed Maria Sakkari defeated Arantxa Rus 6-4 6-4 and fifth seed Caroline Garcia also had few problems against Yulia Putintseva, winning 6-3 6-4.
However, it was not a good day for 10th seed Petra Kvitova, who was beaten 7-6 (11-9) 6-1 by Jule Niemeier, while 13th seed Beatriz Haddad Maia also lost, 7-6 (8-6) 6-3 to Mirra Andreeva and 20th seed Donna Vekic was eliminated in straight-sets by Rebeka Masarova.
Jelena Ostapenko took just 61 minutes to get past Linda Fruhvirtova 6-0 6-3, and will face 14th seed Liudmila Samsonova next, who did not take much longer to see off Maryna Zanevska 6-2 6-3.
There were also wins for Elise Mertens, Badosa, Camila Osorio, Shelby Rogers, Mayar Sherif, Magda Linette and Irina-Camelia Begu.
Svitolina, the top seed at the WTA International event, crushed Arantxa Rus 6-0 6-1 in just 51 minutes in their semi-final.
The Ukrainian lost just nine points on serve and is yet to drop a set at this year's tournament.
Svitolina is into her 17th WTA Tour final and first of 2020, while she will be aiming for her first title since 2018.
Awaiting her in the decider is Marie Bouzkova, who beat second seed Konta 6-3 6-4.
Bouzkova, the Czech ninth seed, saved all five break points she faced to reach her maiden WTA Tour final.
Italian Giorgi battled to take the first set but was pegged back by the home favourite before her game collapsed in a 5-7 6-4 6-0 defeat.
Dominant on serve in the opening set, Giorgi failed to take either of two break points at 3-2 up in the second set. She then won only one point in three consecutive games to allow Garcia to level.
The world number 29 earned just two points on serve in a one-sided decider as Garcia set up a last-16 clash with another Italian, Martina Trevisan.
Earlier, Russian Vera Zvonareva was comfortably beaten by seventh seed Alison van Uytvanck, who could await Garcia in the quarter-finals.
Zhang Shuai beat Kristina Mladenovic 7-6 (7-3) 7-5 to secure a match with Arantxa Rus, who defeated Danka Kovinic for the loss of just two games.
The top-ranked remaining player in the draw, world number 30 Sorana Cirstea, sealed a round-of-16 showdown with Stefanie Voegele after a comfortable 6-3 6-1 defeat of Mariam Bolkvadze.
While she was put to the test in the first round, Raducanu made little fuss as she earned a 6-1 6-2 victory on Court 1.
Raducanu won the first five games of first set, but even after dropping one, she saved a break point to take the opener.
She went on another impressive five-game win streak in the second, with Mertens unable to launch any real counter against the Brit, who was in fine form.
Next up for Raducanu is either Arantxa Rus or Maria Sakkari in the next round.
Data Debrief: Raducanu maintains her high level
Raducanu described her first round victory as "winning ugly" but that was not the case on Wednesday.
Since 2000, the 21-year-old (16-7) is one of only two British female players with a winning record (playing a minimum of five matches) at grand slam events, along with Johanna Konta (39-29).
She is also the third British player in the Open Era to hold a winning percentage of 70% or higher in Women’s Singles Grand Slam matches (70.8%), along with Ann Jones (85.3%) and Virginia Wade (71.3%).
Raducanu is now just one round away from matching her best result at Wimbledon, having reached the fourth round in 2021.
