The outgoing champions trailed 17-0 after half an hour before a yellow card to Heat's Springboks lock Franco Mostert transformed the game.
By the time the South African returned, the Spears had claimed three tries to creep ahead, before running amok during a second-half scoring spree in which they crossed seven times.
After a disappointing defence of their title, the Spears can finish fifth by beating third-placed Tokyo Suntory Sungoliath next week.
Sungoliath were beaten by Toshiba Brave Lupus Tokyo 36-27 in the Fuchu derby.
While the round's other results mean the west Tokyo rivals will meet again in the semi-finals, Brave Lupus will take confidence after completing a season double over Sungoliath for the first time since the 2010-11 campaign.
They did it without trump card, Richie Mo'unga. The All Black, who has been away on bereavement leave, watched from the stands at Prince Chichibu Memorial Stadium.
Yokohama Canon Eagles might have already qualified for the semi-finals, but they were undone by All Blacks fly-half Beauden Barrett, whose visionary kick in behind produced the match-winning try for fullback Taichi Takahashi, following a 31-phase build-up that ran beyond the final hooter.
The try allowed Toyota Verblitz to win the game 35-31, keeping them in contention for fifth going into the final round.
That position is currently held by Dave Rennie's Kobelco Kobe Steelers, and the ex-Wallabies coach's men appear in no mood to surrender it after outclassing Shizuoka Blue Revs 63-19 in Osaka.
Wallaby Quade Cooper missed Saturday's action, but his Hanazono Kintetsu Liners teammates put up a good fight before going down 33-24 to Saitama Panasonic Wild Knights.
Ricoh Black Rams Tokyo, coached by Australian Peter Hewat, will contest next month's promotion/relegation series despite their 31-24 win over Mitsubishi Heavy Industries Sagamihara Dynaboars.
