The Englishman said it was "one of the best laps I've ever done" after he was clocked 1.3 seconds off Nico Rosberg's pole time for Mercedes.
"It was like getting pole position here in 2012; actually probably better," said Button, who was 0.8secs faster than team-mate Lewis Hamilton in 2012.
"This is a tough circuit for us."
McLaren were expecting a difficult weekend in Belgium because the long straights at the Spa-Francorchamps track expose the power deficit of their Honda engine.
But a performance upgrade from Honda for this weekend - said to be worth 0.1-0.2secs a lap - has enabled McLaren to retain their competitive position just inside the top 10.
Team-mate Fernando Alonso had a difficult weekend, however. The Spaniard, who was 0.2secs quicker than Button in final practice on Saturday morning, had a series of reliability problems with the new engine and could not complete a lap in qualifying.
His engine failures mean he will start from the very back with a total of 60 grid places worth of penalties - trumping the 55 amassed by Mercedes' Hamilton, who will start alongside him on the back row.
"It's painful when you have these reliability problems," the two-time champion said, "but it is part of the learning process and we need to understand what is too fragile, reinforce and make sure next year we have an engine capable of fighting for the championship."
Button faces competition for his seat as Alonso's team-mate next year from McLaren reserve driver Stoffel Vandoorne.
The team are poised to decide next month between the two drivers and their dilemma was emphasised this weekend by an intervention from Mercedes F1 boss Toto Wolff, who said it would be "crazy" of the team not to promote Vandoorne.
The Belgian is the most highly-rated driver not in a full-time F1 seat and he out-qualified Button and scored a point on his sole grand prix appearance so far, when he replaced an injured Alonso in Bahrain at the start of this season.
"He deserves a seat in F1," Wolff said. "If guys like Stoffel don't come into F1, the system is wrong."
Button responded: "I did my talking on the track today."
If McLaren choose Vandoorne, Button's 17-year F1 career will come to an end if he cannot find another seat.
BBC Sport understands he has an offer from Williams, who gave him his F1 debut in 2000.
Williams are expected to drop Brazilian veteran Felipe Massa, but are strongly courting Force India driver Sergio Perez and are believed to be close to a deal to sign the Mexican if terms can be agreed. They are also likely to keep Finn Valtteri Bottas.
But even if there is a seat available at Williams, it is not clear whether Button would want to take it. He made it clear this weekend that he only wants to drive on next year if he believes his car will be competitive.
Button is also said to be exploring options in the World Endurance Championship - as he did two years ago when his seat was also in doubt.
However, there does not appear to be a seat for him at the only three factory teams in the premier category there, unless Porsche, Audi or Toyota drop one of their existing drivers. Sources say his only possibility is at Porsche.
McLaren chairman Ron Dennis is said to be strongly in favour of Vandoorne - it is the logical option given the 24-year-old's promise and the fact that Alonso's contract runs out at the end of 2017.
The Spaniard has said he will not decide whether to stay in F1 beyond next year until he has experienced the new cars following a major rule change over the winter.
Button's best option seems to be to try to persuade McLaren shareholder Mansour Ojjeh to back him.
It was the Saudi's intervention that kept Button at McLaren at the end of 2014, when Dennis wanted to retain the Dane Kevin Magnussen, who has since been dropped and is driving for Renault this year.
Ojjeh and Dennis each own 25% of McLaren, with the remaining 50% held by the Bahraini royal family's Mumtalakat investment group.
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Jenson Button said his ninth place on the grid at the Belgian Grand Prix was his best qualifying drive of the season as doubts swirl about his future.