Brian Tuohy scored a hat-trick of tries as Connacht recorded their biggest victory in Europe.
Fly-half Ian Keatley helped himself to 26 points through a penalty, try and nine conversions. Niva Ta'auso also scored a brace of tries as the Irish province crossed the whitewash 12 times with Michael McCarthy, Fionn Carr, Sean Cronin, Mike McComish, Adrian Flavin, Ray Ofisa also going over.
Noah Soqueta's 12th-minute try was all Prato could muster, with Alberto Chiesa adding the conversion.
Harlequins booked their place in the knockout stage as a strong second-half showing secured the 2001 and 2004 tournament winners a home quarter-final but the Londoners were made to work for the victory.
A brace of tries from livewire centre George Lowe proved the turning point after the visitors led 14-13 at half-time at The Stoop. Lowe crossed twice inside seven minutes to give Quins a decisive lead, ghosting through some poor Bayonne defence just 40 seconds after the restart before showing his pace with a classy outside break with 47 minutes on the clock. Nick Evans kicked 14 points, scored a superb individual try and made another for England and Lions wing Ugo Monye.
Evans set Quins on their way with only five minutes played but Bayonne hit back with a Ross Filipo score and three penalties from Cedric Garcia to lead by a point at the break. Lowe then struck twice in quick succession before Monye scored with eight minutes remaining. Sam Smith added a fifth with the last play of the game.
Sale rounded off their Challenge Cup in style with an eight-try, 50-5 win against Cetransa El Salvador. Centre John Kennedy scored twice in the first half to set the Sharks on course for a straightforward win at Campo de Pepe Rojo. Rob Miller converted five tries, including his own, to finish with 15 points but the win came too late to keep the Sharks' European hopes alive.
Uale Mai responded for the hosts with a 13th-minute try but Mathew Tait and Fergus Mulchrone also crossed in the first half as the Sharks took little more than half an hour to bag a bonus point. The second half became a formality after Miller took just five minutes to slip through for Sale's fifth.
Sale rung the changes and three replacements stepped off the bench to join the scoring. Kyle Tonetti touched down after 56 minutes, followed by Chris Jones and Lee Imiolek as Sharks hit the half-century mark with the last attack of the game.
However, Sale still finished second in Pool Two, six points behind
A late Quentin Doumayrou try saw Montpellier break Exeter hearts and reach the quarter-finals at the expense of the English club with a 32-30 home win.
Exeter had led 30-25 after tries from Luke Arscott and Matt Jess (two) plus 15 points from the boot of Ryan Davis.
Montpellier's Raphael Legarde kicked six penalties and converted a try from Goderzi Shvelidze, before Doumayrou struck and Legarde added the extras to dump the Chiefs out of Europe.