Facing two ‘lucky losers’ from qualifying, Ariel Behar of Uruguay and Belarus’s Alexander Bury, they recorded a 6-4 6-3 5-7 6-4 victory on Court 9.
Behar and Bury saved two break points at 3-4 down in the first set but Daniell took the next one in style, hitting the baseline with a deep volley to win the first set.
Daniell – coached by Dave Sammel and Ian MacDonald at the Sports Training Village – and Demoliner stamped their authority by breaking in the second game of the next set, which they went on to win 6-3.
They suffered a setback in the third set when, having saved three break points in the 11th game, Behar and Bury forced their only one of the match at 6-5 up and went on to take it.
Daniell received medical treatment before the fourth set but he and Demoliner quickly regained the initiative by breaking in the third game before seeing the match out without any further scares.
They will now face Australian duo Thanasi Kokkinakis and Jordan Thompson, who won their first-round match with three tie-breaks.
Daniell is also playing in the mixed doubles this year with Croatia’s Darija Jurak – they meet Mate Pavic and Lyudmyla Kichenok in the first round later this week.
Two more Team Bath MCTA players are scheduled to be in mixed doubles action at SW19 on Saturday. Anna Smith, who lost in the first round of the women’s doubles, will partner Neal Skupski against fellow Brits Joe Salisbury and Katy Dunne, while Liam Broady will partner sister Naomi against Belgium’s Steve Darcis and Elise Mertens.