Italian reports suggested Senna would be paired with Britain's Jenson Button for 2009, leaving Button's 2008 team-mate Rubens Barrichello, of Brazil, without a drive for the new season.
Brawn oversaw all seven of Michael Schumacher's world titles in addition to Jenson Button's in 2009.
Ferrari were quick enough in Monaco that Brawn's race day victory effectively hung on Button's near-perfect qualifying lap.
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Vettel, who sits third behind England's Button and Brazil's Barrichello in the drivers' championship, was forced to end his opening session early after smoke came from his car, but he finished sixth, 0.604secs off the pace, in the afternoon.
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Button's Brawn GP team-mate Rubens Barrichello finished behind the dominant Red Bulls in third place, to close to within 23 points of Button in the world drivers' standings, with Vettel breathing down the Brazilian's neck.
The result also means that Button's Brawn GP team have claimed the constructors' title.
Ferrari were not competitive in the first session, when Alonso was 0.850secs off Button's pace.
Button's team-mate Rubens Barrichello scraped through into the second session but could manage only 14th place.
BBC: Hamilton edged out Ferrari's Kimi Raikkonen by 0.102secs
Button's team-mate Rubens Barrichello endured an incident-packed race but was impressed with the Brawn's durability.
Button's playboy lifestyle in his early F1 career didn't fit well with the mores of the sport, either.
That positioning was a result of the very small but decisive pace advantage of Button's Brawn in qualifying.
The German was 0.356secs ahead of Button's McLaren in third, with Massa, Vettel, Alonso and Hamilton were next up.
BBC: Lewis Hamilton fastest in Friday Australian GP practice
It is believed that Button's management have taken advantage of clauses in engine supplier Honda's new contract with BAR.
BBC: SPORT | Motorsport | Formula One | BAR set Button deadline
As long as they continue to out-score the Brawns slowly but surely they are eating into Button's 21-point lead.
The highlight of this second era running its own team was Jenson Button's win at the 2006 Hungarian Grand Prix.
With only three laps before his own stop, Vettel had nowhere near enough time to try to erode Button's advantage.
Button's McLaren started fourth on the grid, as Red Bull's Sebastian Vettel set the pace in qualifying to claim pole position.
But Button's team-mate Rubens Barrichello insists his felllow Brazilian has not changed.
Fernando Alonso produced a stunning lap to grab pole, while team-mate Felipe Massa qualified third fastest behind 2009 champion Jenson Button's McLaren.
In contrast, Button's choice of the regular set-up will give him more stability on corner entry and help him to protect his tyres.
Button's team-mate Lewis Hamilton admitted that traffic problems were likely, but said it was still possible to put in a good lap time.
Barrichello was fifth, a three-stop strategy not working out for Button's team-mate, ahead of the Ferrari of Kimi Raikkonen, Glock and Fernando Alonso's Renault.
Button's team boss, Ross Brawn, said the team were planning updates to their car for the Spanish Grand Prix at Barcelona's Circuit de Catalunya.
The German found himself under investigation at the start of the race after he cut off Button's attempt to pass him off the line.
Button's compatriot and out-going world champion Lewis Hamilton came home third.
The other drivers to take part were Button's former Brawn teammate Rubens Barrichello in a Williams, Toro Rosso's Sebastien Buemi and Renault's new signing Robert Kubica.
Button's victory in Melbourne capped a remarkable reversal of fortunes for the team, but the legal wrangling threatened to dampen their celebrations before Wednesday's conclusive ruling.
Davidson, who tested for BAR last season, was promoted to third driver after Sato succeeded former world champion Jacques Villeneuve as Button's team-mate for the 2004 campaign.
BBC: SPORT | Motorsport | Formula One | Davidson eyes 2005 race seat
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