Underdogs Durham made an impressive 312 for 5 off their 50 overs in their first appearance in an English domestic final. Hampshire scored 158-5 off 32.3 overs before rain forced the match to go over into a second day.
Hampshire captain Warne, 37, won the toss and elected to field.
But the north-eastern county took full advantage as Shivnarine Chanderpaul (78), Kyle Coetzer (61) and captain Dale Benkenstein (61 not out) helped rack up a daunting target.
Hampshire's West Indies fast-medium bowler Daren Powell took two wickets for 80 runs in his 10 overs, while leg spin legend Warne took no wickets for 46 runs from his.
Then Durham quick Ottis Gibson took wickets with his first two balls and had England batsman Kevin Pietersen out leg before wicket for 12 to leave Hampshire reeling.
When play was called off, Nic Pothas was 39 not out off 43 balls and Dimitri Mascarenhas was three not out off five balls.
Of the Durham bowlers, Gibson led the way with three wickets for 24 runs off eight overs.
Hampshire need nearly nine runs per over if they are to stage one of the greatest comebacks in Lord's finals history.
Warne defended his decision to put Durham in to bat.
"We didn't bowl as well as we thought we could," he said.
"We thought we could have got two or three cheap ones early, put the pressure right on Durham, and we thought the chasing as well, with the small boundary out there, it's hard to defend.
"With the rain coming in later on, I think all the decisions that we made were pretty right it was just we didn't execute them well enough. To Durham's credit, they played exceptionally well.
"We're all capable of slogging a few hopefully so we're not out of it yet. It's going to be an unbelievable victory if we can, but a new day, you just never know."
Durham 312 for 5 in 50 overs (Chanderpaul 78, Benkenstein 61, Coetzer 61, Mustard 49; Darren Powell 2 for 80, Sean Ervine 1 for 34, Bruce 1 for 43) Vs 158 for 5 in 32.3 overs (John Crawley 68, Nic Pothas 39 n o, Carberry 23;Otis Gibson 3 for 24,Collingwood 1 for 15). Match will resume today (Sunday).