The wicketkeeper, averaging over 70 runs per innings for the series, put on 104 for the sixth wicket with Steve Smith, who was unbeaten on 48 at the break, at a Sydney Cricket Ground bathed in summer sunshine.
Australia, looking to wrap up a 5-0 series sweep, had looked well and truly on the ropes when England struck twice in the 15 minutes before lunch and then dismissed George Bailey for one shortly after the resumption.
Haddin, as he has in all four previous Tests when his team were in similarly precarious positions, came out oozing positivity and took the game to the bowlers with a barrage of aggressive strokes.
England contributed to their own demise by bowling short to a batsman who was clearly happy to pull to the boundary all day with Ben Stokes (2-62) suffering particular punishment, including three Haddin fours in one over.
The torment for the tourists only deepened when tall Irish paceman Boyd Rankin, one of three new caps in the side, hobbled off the field with what looked like a left hamstring strain.
Haddin reached his fifth half century of the series from 70 balls 15 minutes before tea with a hurried single past Stokes, having hit eight of his 10 fours in another important knock.
The day had started well for England when captain Alastair Cook won the toss for the first time in the series and chose to send his new-look team out to bowl on a green-tinged wicket under overcast skies.
David Warner (16), Chris Rogers (11) and Australia captain Michael Clarke (10) and Shane Watson (43) were then all dismissed as England claimed the honours in the opening session.
The first reward for Cook's gamble came in the sixth over when Stuart Broad removed Warner with a peach of a delivery that smashed into the top of the batsman's off stump.
There was no perceptible swing, though, and as the cloud over the newly-developed ground cleared, it looked like Australia just had to weather the new ball.
All-rounder Ben Stokes pegged them back in the 16th over, however, when opener Rogers misjudged the length of a delivery and chopped the ball onto his own stumps to leave his side two down with 51 runs on the board.
When it looked like Australia might make it through to lunch without further loss Stokes struck again by finding a good length and inducing Clarke into a thick edge which Ian Bell claimed in the slips.
Better was to follow and, with the break looming, Anderson hit Watson on the front pad with successive deliveries and the umpire raised his finger after the second to make the all-rounder the first Australian batsmen in the series to fall lbw.
After four humiliating defeats, England rang the changes in their team by dropping top order batsman Joe Root, spinner Monty Panesar and seamer Tim Bresnan.
In their place, first caps were awarded to batsman Gary Ballance, young leg-spinner Scott Borthwick and Rankin.
While England have now used 18 players on the tour, Australia were unchanged for the fifth successive Test in the series.