Speight scored twice for the home side as they notched a bonus-point by scoring four tries before halftime and jumped to the top of the table on 40 points.
Their victory ensured they also took hold of the Australian conference ahead of the Queensland Reds (37).
"We had an extremely strong first 20 minutes that set us up for the game," Brumbies captain Ben Mowen said. "We know what end of the comp this is now and we know that we can't have a down week."
Speight scored both of his tries in the first half as the Brumbies produced patient, clinical rugby on attack and ruthless aggression on defence.
The pack secured possession, the ball runners like Mowen and fellow loose forward Fotu Auelua punched over the advantage line or through the defence and then once the Force players had been committed in close, they spun it wide.
Fullback Jesse Mogg and Tevita Kuridrani also scored first half tries for the home side, while inside centre Christian Lealiifano slotted three conversions - two from the right hand touchline - and a penalty to give them a 29-0 lead at the break.
With the game in the bag the Brumbies buttoned off but were still dominant after the break, no more exhibited when winger Joe Tomane scored his side's fifth try despite having hooker Stephen Moore in the sinbin.
Brumbies replacement hooker Siliva Siliva scored his first Super Rugby try before the Force finally converted one of their opportunities on attack when captain Matt Hodgson grabbed a consolation try in the final 10 minutes.
The Waikato Chiefs jumped out to a 24-0 lead inside the first quarter then withstood a ferocious counter-attack from the Sharks to record a 37-29 victory in their match in Hamilton.
The Chiefs had lost their two previous games after some poor play but the bonus-point victory moved the 2012 champions to 35 points and back in charge of the New Zealand conference ahead of the Auckland Blues (32).
The Chiefs had looked like they would run away with the game after a high-tempo start, racing out to a 24-0 lead inside 20 minutes with tries to Asaeli Tikoirotuma, Bundee Aki and Tim-Nanai Williams.
Tikoirotuma and Aki's tries came from well worked moves off set pieces and Nanai-Williams scooped up a dropped ball and sprinted more than 50 metres.
Fullback Gareth Anscombe, who had slotted an early penalty, converted all three tries to give the home side a lead that looked insurmountable.
"We had a really fast start and maybe we thought it was too easy," Chiefs captain Craig Clarke said. "Disappointing from our point of view to let them come back but they showed a lot of fight."
The Sharks used their massive pack to great effect and set up a well-drilled rolling maul to allow Derick Minnie to crash over before number eight Lubabalo Mtembu scored his first Super Rugby try following an attacking scrum.
Minnie added his second, again from an attacking lineout and rolling maul, just before halftime to reduce the deficit at the break to 24-19.
The Chiefs pulled ahead again early in the second half with Nanai-Williams scoring his second try after the Sharks defence failed to control an Aaron Cruden grubber kick and the centre flopped on the ball over the line.
Anscombe converted and added a penalty to give the Chiefs a 34-19 lead before the visitors again stormed back with Keegan Daniel crossing after superb buildup work from both backs and forwards.
Sharks flyhalf Patrick Lambie, who had kicked three conversions, added his first penalty with two minutes remaining but the visitors conceded a penalty just as the hooter sounded and Cruden slotted the kick to deny them a second bonus point for finishing within seven points.
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