Skegness were bowled out for 186, Rhett Bridgens and Adi Sreedharan taking four wickets each.
Curtis then hit an unbeaten 75 after coming to the crease with the score on 73 for two and added 87 with Matt Smith.
Smith, who had shared a second wicket stand of 66 with Phil Brown, was out for 66 but Curtis saw his team home for the loss of five wickets.
Grantham and Market Deeping now top the table, the only sides with maximum points.
Grantham scored a comprehensive victory over Sleaford but Deeping were involved in the tightest game of the day, winning by one wicket after chasing just 121.
Zac Simmonds took four Lindum wickets but it was Mel Adatia who kept the visitors’ run rate down, bowling 17 overs with eight maidens and taking two wickets while giving away only 16 runs.
Wicketkeeper David Sargeant contributed five dismissals, including two smart stumpings and Deeping’s pursuit set off well, until 53 for two quickly became 61 for five, Jonny Miller and Matt Rutherford doing the damage.
Sargeant and David Gillett got the innings back on track and at 101 for six, Deeping were on the road to victory.
But Miller and Rutherford struck again and a run out made it 108 for nine.
However, Sargeant was still at the crease and he and Simmonds saw their side home, the wicketkeeper ending on 22.
Dan Freeman and Dan Webb each hit 59 of Grantham’s 257 for nine and Freeman went on to take four wickets as Sleaford were all out for 122.
Bracebridge Heath also made 257 for nine, Nick John falling just two short of his century and Brett Houston hitting 45 in a second wicket stand of 116 with John.
Houston then reduced Woodhall Spa to 11 for two, bringing Tanveer Sikander to the crease.
By the time Sikander was caught off Houston, he had made 113 off 98 balls and Woodhall were 204 for eight but the overs were running out and the innings ended on 205 for nine and a share of the point for the visitors.
Bourne struggled for runs at Boston, losing their first two wickets for 12 runs, but were rescued by a good innings from Ben Stroud who hit 78 of his side’s 185 for nine.
Stroud and Carl Wilson (28) put on 60 for the third wicket and Jack Berry contributed 22 lower down the order, while Tom Baxter claimed five wickets for Boston.
Berry then opened the bowling and went on to take four wickets as Boston were all out for 63, only Michael Musson reaching double figures with 28.
Water under the covers at London Road reduced Louth’s game against Grimsby to 64 overs, the home side making 132 for eight, a total Grimsby overtook for the loss of seven wickets, leaving Louth at the bottom of the table.
Results: Bracebridge Heath 257-9 (John 98), Woodhall Spa 205-9 (Sikander 113); Bourne 185-9 (B Stroud 78, Baxter 5-38), Boston 63; Lindum 121 (Adatia 17-8-16-2, Sargeant 5 w/k dismissals), Market Deeping 122-9; Grantham 257-9 (Freeman 59, Webb 59), Sleaford 122; Skegness 186, Nettleham 190-5 (Smith 66, Curtis 75no); Louth 132-8, Grimsby 134-7 (game reduced to 64 overs).