Matters were less straight forward in Pool Four for Newcastle who struggled at Overmach Parma before replacement John Rudd saved the Falcons with a late try, converted by teenager Rod Miller.
Danny Williams looked to have put Newcastle on course with a first half try before Scottish fly-half Barry Irvine kicked Parma into a surprise lead. The match ended 20-14 to the English team.
Connacht were also made to work hard for success in Italy, at Rovigo in Pool One, before Frank Murphy scored his second try to complete a 35-20 win. Viadana, Saracens rivals in pool Five, claimed a vital away win, 21-15 at Mont de Marsan.
In the evening match, Saracens laboured to a 16-6 win over Bayonne at the Stade Jean Dauger. Census Johnston's late try was the only time the whitewash was breached in a tense 80 minute cross-channel battle.