Ponting - who passed Rahul Dravid to become the second highest scorer of Test runs during his innings of 23 - and Michael Clarke (24) both fell caught in close as Shillingford extracted bounce and turn from the Windsor Park wicket.
Then came the highlight of the day when Sammy took a diving one-handed catch at slip to remove Hussey (10) and give Shillingford his fourth wicket.
Kemar Roach (1-43) ensured all four Windies bowlers ended the day with a wicket when he removed Ryan Harris (4) but Warner felt Starc and Wade's partnership could prove vital.
"If we can get 250 it's probably par, then we've just got to sum it up in the second innings,'' Warner said.
"I reckon day four or day five, chasing 200 or 250 is going to be very tough for either team.''
Shillingford said the Windies were hoping to keep Australia under 250 when play resumes.
"I wouldn't say they got away,'' Shillingford said.
"Cricket is a patient game. It's not where you can just go blasting batsmen.
"The guys were positive as well so it's a matter of coming back tomorrow and taking them out as quick as possible.''
- AAP