Wallabies fullback Kurtley Beale, returning from a month-long suspension due to an alcohol-fueled fight with two team-mates in South Africa, came off the bench to score one of the Rebels' five tries and help set up another.
But Brodie Retallick's try following his block of an attempted clearing kick by Rebels flyhalf James O'Connor with eight minutes left ultimately gave the New Zealand Conference-leading Chiefs their winning margin.
GALLERY: Super Rugby - Week 12
Lock Hugh Pyle scored a pair of tries for the Rebels, who trailed 24-14 at half-time but had more than 80 percent possession in the second half.
The Chiefs scored four tries in the opening half - three by Anscombe. A fourth try at the end was disallowed by video.
Beale,
who still hopes to play for Australia against the British and Irish
Lions in three tests in June and July, had missed the last six games;
first through a broken hand and then suspension for his drunken
altercations.
After undergoing counseling over the past month, he returned to training on Tuesday and was named in the reserves a day later.
He came on at fullback in the 47th minute and made an inauspicious start; kicking the ball out on the full in the restart. But he showed he had lost none of his electric pace and skills as he helped set up lock Pyle's second try.
He and fellow playmaker O'Connor
combined to send Nick Phipps in under the crossbar before Beale split
the defense and raced to the tryline himself in the 75th, giving the
Rebels two bonus points despite the loss.
Rebels:
15 Jason Woodward, 14 Tom English, 13 Mitch Inman, 12 Rory Sidey, 11 Cooper Vuna, 10 James O'Connor, 9 Nick Phipps, 8 Scott Higginbotham (captain), 7 Scott Fuglistaller, 6 Jarrod Saffy, 5 Cadeyrn Neville, 4 Hugh Pyle, 3 Laurie Weeks, 2 Ged Robinson, 1 Nic Henderson
Substitutes: 16 Shota Horie, 17 Paul Alo-Emile, 18 Luke Jones, 19 Gareth Delve, 20 Nic Stirzaker, 21 Kurtley Beale, 22 Lachlan Mitchell
Chiefs:
15 Gareth Anscombe, 14 Lelia Masaga, 13 Tim Nanai-Williams, 12 Bundee Aki, 11 Asaeli Tikoirotuma, 10 Aaron Cruden, 9 Brendon Leonard, 8 Matt Vant Leven, 7 Sam Cane, 6 Liam Messam, 5 Brodie Retallick, 4 Craig Clarke (captain), 3 Ben Tameifuna, 2 Mahonri Schwalger, 1 Pauliasi Manu
Substitutes: 16 Hika Elliot, 17 Toby Smith, 18 Michael Fitzgerald, 19 Tanerau Latimer, 20 Augustine Pulu, 21 Robbie Robinson, 22 Patrick Osborne