The Canadian-born British No 2 now meets the experienced Frenchman Cedric Pioline for a place in the semi-finals. The last Briton to achieve that was Yorkshire's Roger Taylor, who lost to Bjorn Borg.
Rusedski is linked with Yorkshire inasmuch as his mother was born in Dewsbury, but there can be little doubt of his commitment to the national cause since his transfer from Montreal in 1995.
No sooner did he arrive than he embraced the flag, winning a place in the last 16, at which point he was defeated by Pete Sampras.
On this occasion, Rusedski hopes to enjoy an extended run. "I've got a difficult match against Cedric Pioline," he said. "It's his third time in the quarters. He returns extremely well, and I think he's going to mix it up, stay back and come in, and do a bit of everything.
"It's going to depend on how well I serve and how well I return. I have to return a little bit sharper than I did today, and I am going to have to hit my ground shots and work the point a bit more."
Rusedski was far happier at his work than during Saturday's second-round match against another American, Jonathan Stark. Worried by a niggling back injury, Rusedksi vented his frustrations on the umpire after a disputed call.
Sunday's straight-sets victory against Andrew Richardson, a compatriot, set the tone for yesterday's performance. "I think I was better focused," Rusedski said.
"My back was really sore on Saturday, and I wasn't in such a good mood. My physio has done a tremendous job, and I'm feeling very good. You have those days where you're not always playing your best tennis, and sometimes you do silly things out there to get yourself going.
"I'm pleased I took advantage of the situation today. I think that was one of the best matches I've ever served."
Rusedski barely had time to loosen his left arm before drizzle forced the players back to the locker-room for 17 minutes, after which the British No 2's serving was as relentless as Friday's rain.
He hit 32 aces, a total of 61 service-winners, and won 90 per cent of the points on his first deliveries. His volleys were pretty fair, too, 15 of them producing winners.
Although Reneberg managed to save the solitary break-point in the opening set, improvising a defensive drop-volley in the sixth game, he was overwhelmed in the tie-break, 7-2, feeding Rusedski encouragement he scarcely required by double-faulting to 1-5.
An impressive return by Rusedski tilted the second set his way on his second break-point at 2-2, and he secured the two-set lead after 74 minutes with an ace on the first set-point.
Reneberg might have begun to despair of ever cracking the Rusedski serve after being bamboozled by three aces and a service winner in the fourth game of the third set, by which time a similarity in the pattern of points may have lulled some spectators into a midday slumber.
If so, they would have been rudely awakened by one of the biggest cheers of the match, in response to a splendid catch by a woman in pink when a ball was deflected high into the stands off the frame of a racket. A luminous green plastic bracelet suggested that the spectator was a happy camper from the overnight queue, and her dexterity brightened the day.
The only time Rusedski appeared to be in the remotest danger of being extended beyond straight sets was when he was taken to deuce at 5-6, Reneberg reading a second serve to his backhand and driving it across the court. He then netted a return and scarcely saw the ace with which Rusedski guaranteed a second tie-break.
Reneberg missed a forehand to put his opponent at 5-4 with two serves to come. The American returned one of them over the baseline, Rusedski finishing the job on the first match-point with an ace off a second serve.
This was greeted by an explosion of cheering, Union Jacks of various sizes materialising as it dawned on the crowd that another Brit had become a member of the Last Eight Club.
Had Rusedski noticed the empty seats early in the match? "I didn't really," he said. "The crowd that came to watch the match were terrific. They were very supportive. And, I mean, it's lunch hour, 12 noon, so I guess they're off to lunch." Some might even be out to lunch if the success story continues.
"I'm very pleased to be in the quarter-finals, but I don't want to stop here," Rusedski said. "This, hopefully, is just the beginning."
Boris Becker, defeated the Chilean Marcelo Rios, seeded one place below him at No 9, to head a trio of victorious Germans into the last eight. The other two are unseeded. Michael Stich we know. He defeated Becker to win the title in 1991.
The other one, Nicolas Kiefer, we are likely to learn much more about as time goes by. Due to celebrate his 20th birthday on Saturday, and ranked No 98 in the world, he eliminated the third-seeded Yevgeny Kafelnikov, 6-2, 7-5, 2-6, 6-1.
Two years ago, Kiefer was the runner-up in the junior singles. Two weeks ago he played Kafelnikov for the first time, on a grass court at Halle, and was beaten, 7-6, 7-6.
Yesterday, the Russian found himself two sets in arrears before he was able to make an impression. Kiefer, unlike Tim Henman in the first round last year, did not allow Kafelnikov's prospects of a revival to linger much longer than the third set.
Kiefer's reward is a quarter-final against Australia's Todd Woodbridge, who defeated a compatriot, the 12th-seeded Pat Rafter, 6-7, 6-4, 7-6, 6-3.
Stich who is playing his last Grand Slam tournament, defeated Australia's Mark Woodforde, 6-4, 6-7, 6-3, 7-5.Reuse content