At lunch on the fourth day of the third Test at the Waca Ground on Sunday, England were 99 for one in their second innings, as the pair defied the Australian attack to keep England's hopes alive.
England resumed at 19 for one, and overnight batsmen Bell and Cook boosted the visitors' spirits by lasting through to lunch to be not out 54 and 37 respectively.
England are chasing 557 to win or need to bat out the match to earn a draw and keep alive their chances of retaining the Ashes. Australia are currently 2-0 up in the five-Test series.
On another warm day in Perth, Bell batted with the purpose the English lacked in the first innings and produced some attractive strokes, twice lofting champion leg-spinner Shane Warne down the ground for six.
Bell reached his half-century when he advanced at Warne and thrashed the ball through cover for four despite being beaten in flight.
He faced 83 balls for his 50 and hit five fours and two sixes.
The left-handed Cook, a promising player still searching for his first significant innings of the series, was more circumspect.
The pair had the odd anxious moment when Warne, with 695 Test wickets, was introduced midway through the session, but they were able to keep the veteran at bay despite some sharp turn.
Cook enjoyed some good fortune in the next-to-last over before lunch.
He pulled Warne towards Glenn McGrath on the deep mid-wicket boundary but the veteran paceman judged the flight of the ball poorly and moved in, only for the ball to float over his head and bounce once before going over the boundary rope.
There was little assistance from the wicket for Australia's fast bowling trio of McGrath, Brett Lee and Stuart Clark, with just the odd ball climbing more than expected off the pitch.
The only batsman out for the English was Andrew Strauss, adjudged lbw by Rudi Koertzen for a duck when he padded up to Lee late on the third day.
Australia 1st innings: 244 (M. Hussey 74 not out, M. Panesar 5-92, S. Harmison 4-48)
England 1st innings: 215 K. Pietersen 70
Australia 2nd innings: 527-5 decl (M. Clarke 135 not out, M. Hussey 103, A. Gilchrist 102 not out)
England 2nd innings: 99 for 1 (A. Strauss lbw b Lee 0, A. Cook not out 37 I. Bell not out 54, Extras nb5, w1, lb2)
Fall of wkt: 1-0
Bowling: Lee 9-2-20-1 (1nb), McGrath 11-3-27-0 (4nb 1w), Clark 6-3-9-0, Warne 8-0-41-0