Errani and Vinci are the top seeds in the women's doubles but quickly fell a set behind as the Williams sisters claimed the opener 6-3 with some ferocious hitting at the baseline.
A tight second set went all the way to a tie-breaker but it was the Italians who stayed strong to level the match with a comfortable 7-1 win in the breaker.
Unforced errors crept into Serena and Venus's game under pressure in the tie-break and they became commonplace as both teams tightened up in a tense third set.
Each duo traded breaks of serve until Errani and Vinci had a chance to serve for the match at 5-4, but the Williams sisters dug deep to break and stay alive.
Just as the tide seemed to be turning Venus produced a pair of untimely double faults to hand her opponents another break, and this time the Italian pair made it count.
The top seeds served out the match 3-6 7-6(1) 7-5 to send Serena and Venus packing in the quarter-finals and end Venus Williams's involvement at this year's Aussie Open.