Marray, on the other hand, gave a mixed performance, double faulting twice and missing a couple of volleys when he and Daniell looked to have the second set under control.
There was early disappointment for Daniell's Davis Cup teammate Artem Sitak who teamed up with Jonathan Erlich of Israel.
They lost their first round match 7-6, 3-6, 7-6 to the Italian combination of Andreas Seppi and Marco Cecchinato after spending more than two hours on court. Seppi and Cecchinato won 7-4 in the final tiebreaker.
The second round match between Daniell and Marray and Phillip Oswald (Austria ) and Adil Shamasdin (Canada) was a see-saw affair with Oswald and Shamasdin eventually taking the honours 4-6, 6-4, 7-6.
Daniell was left ruing opportunities after the close-fought affair.
"I don't think anyone out there today felt like they played well, it was an ugly battle," he said. "There are definitely positives from getting through the first round match and competing. "But the disappointing thing is Jonny and I knew we could win it but we didn't step up, and that's a little bit hard to stomach."
Daniell's effort should earn him enough ATP ranking points to move him inside the top 70 ranked doubles players in the world and he also took away just over US$10,000 ($15,000) in prize money.