Sapsford, who considered himself fortunate to receive a wild card for the event, reached the first ATP Tour quarter-final of his career when he beat the seventh seed, Juan Albert Viloca of Spain, 7-5, 7-5 in the first match on the Centre Court.
Then Rusedski, the sixth seed, overcame an uncertain start to defeat the Argentine left-hander Daniel Orsanic 6-4, 6-4 in 72 minutes.
Their joint appearance in the last eight was the best British performance on clay since Jonathan Smith, Robin Drysdale and Mark Cox all reached the last eight, also at Bournemouth, in 1980.
Sapsford, ranked 181, had to grind out his win against Viloca, an out- and-out baseline player ranked 81. Sapsford said: "I kept thinking I would like to go in and volley, but it is difficult when your opponent hits such good ground strokes.
"But it's great for me because I was not expecting a wild card. I'm 27 and I thought my age was against me. I thought the wild cards would go to youngsters."
Rusedski won his battle with Orsanic after going 3-0 down in the first set. Orsanic broke Rusedski in the second game, but that was his only success.
As the match wore on Rusedski, who broke back in the fifth game, served better and better. He broke Orsanic again in the ninth game before serving out for the set. Games went with service until the ninth of the second set before Rusedski broke through and then held his own serve for victory.
"I was trying to end points too quickly in the first three games," Rusedski said. "But then I found my rhythm and, perhaps more importantly, I took more time before I went into the net."
Australia suffered a blow in their attempt to rejoin the Davis Cup world group when injury forced the break-up of their specialist doubles pairing of Todd Woodbridge and Mark Woodforde. Woodbridge has withdrawn from the world group qualifying tie against Croatia in Split next week to undergo minor surgery.Reuse content