The pair both registered three wins from three matches to surge to the top of the group on the third day of play at Crondon Park Golf Club.
Carter, the world number 14, beat Mark Davis 3-0 and then Stuart Bingham by the same scoreline before edging Martin Gould 3-2 in his final match.
Australia's world number five Robertson, meanwhile, beat Stephen Maguire 3-1, Bingham 3-0 and Judd Trump 3-1 to keep pace with his rival.
Gould ended the day with a 2-2 record, after hitting the day's highest break of 133 in his 3-2 win over Judd Trump.
Twenty-five of the world's top players are competing in the Championship League, the Premier League qualifying event.
Seven groups of seven players produce seven winners who play in one further group in March to determine the winner who will play in the 2013 Premier League.
In each group the top four players from the round robin stage will contest the semi finals and final over the best of five frames.
The players coming sixth and seventh in the group will be relegated and will not feature in any further group matches and therefore three players will leave and be replaced by a further three players.
Group 2 matches
Ali Carter 3-0 Mark Davis
Stephen Maguire 1-3 Neil Robertson
Mark Davis 2-3 Martin Gould
Neil Robertson 3-0 Stuart Bingham
Mark Davis 2-3 Judd Trump
Martin Gould 0-3 Stuart Bingham
Martin Gould 3-2 Judd Trump
Stuart Bingham 0-3 Ali Carter
Judd Trump 1-3 Stephen Maguire
Ali Carter 3-2 Martin Gould
Stephen Maguire 1-3 Stuart Bingham
Neil Robertson 3-1 Judd Trump
Group 1 - Judd Trump, John Higgins, Shaun Murphy, Ali Carter, Matthew Stevens, Mark Davis and Martin Gould
Group 2 - Four players from Group 1 (Carter, Gould, Davis and Trump) plus Stephen Maguire, Neil Robertson and Stuart Bingham
Group 3 - Four players from Group 2 plus Mark Selby, Mark Williams and Ding Junhui
Group 4 - Four players from Group 3 plus Ricky Walden, Mark Allen and Barry Hawkins
Group 5 - Four players from Group 4 plus Joe Perry, Peter Ebdon and Ryan Day
Group 6 - Four players from Group 5 plus Marcus Campbell, Marco Fu and Dominic Dale
Group 7 - Four players from Group 6 plus three Andrew Higginson, Tom Ford and Robert Milkins
Winners' Group - Winners of groups 1 to 7