Elliot's try extended the score to 22-9 at the break, though until that point the game had been in the balance with Ihaia West slotting three penalties and missing two.
Liam Messam and Damian McKenzie had also scored first half-tries for the home side before Lachlan Boshier, James Lowe and Anton Lienert-Brown, who finished off a sweeping 80-metre movement, all crossed to give the Chiefs a 41-9 lead.
The Blues, who had appeared shell-shocked for the first 10 minutes of the second half were bolstered by coach Tana Umaga when he introduced a raft of All Blacks off the bench.
The experience of players like Jerome Kaino and Charlie Faumuina settled the visitors down and the Blues had the better of the final quarter, despite being a man down.
Lock Patrick Tuipulotu, prop Faumuina and utility back Rene Ranger all crossed to get the visitors within touching distance and give the Chiefs some nervous moments in the final 10 minutes.
The home side, however, again settled and managed to wind down the clock by controlling field position and the ball without being able to crack the Blues defence again.
All Blacks flyhalf Aaron Cruden, playing his 100th Super Rugby match, slotted four conversions and a penalty for the Chiefs, who clinched the bonus point by scoring the six tries.
"I actually had my first game in 2010 against the Blues so it was quite special to bring up the ton against them," Cruden said. "We were good in patches but in saying that there are still things to work on."
(Reporting by Greg Stutchbury in Wellington; Editing by Amlan Chakraborty)
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