The Australia skipper, enjoying an inspired 2012, surpassed the 1,544 runs Ricky Ponting amassed in 2005 during his innings of 106, before tail-ender Mitchell Johnson rubbed salt into Sri Lanka's wounds with an unbeaten 73.
Paceman Johnson strode off at stumps with Nathan Lyon yet to score, with Australia having added 108 runs in the session after tea to drive their total to an imposing 440-8 at the Melbourne Cricket Ground.
"As many runs tomorrow would be very handy," Clarke said after celebrating his first ton at the MCG.
"I would love to see Mitchell get his second Test hundred and then we'll be back out there bowling and hopefully we can bowl Sri Lanka out."
Sri Lanka, skittled for 156 on day one, had only a six-run lead to protect at the start of the day's play and their hopes of restricting the hosts diminished with a hamstring injury to seamer Chanaka Welegedera in the morning session.
The remaining bowlers had little assistance from a flattening pitch on a gusty day and were put to the sword by Clarke and Shane Watson, who composed a record-breaking fourth-wicket stand of 194 against Sri Lanka at the MCG.
Clarke's fifth Test ton of the year, the 22nd of his career, propelled him to 1,595 runs for the year and fourth on the all-time list behind Mohammad Yousuf (1,788), Viv Richards (1,710) and Graeme Smith (1,656).
Clarke's selection appeared a gamble after he sustained a hamstring injury in the first-Test victory in Hobart, and pundits complained that it was a case of double-standards given injury-free seamer Mitchell Starc was left out as part of the team's controversial rotation policy.
Few would be arguing after Thursday, with Clarke's 14-boundary knock confounding the Sri Lankans for more than four hours and putting Australia in the box seat to take a winning 2-0 series lead before the final Test in Sydney.
The 31-year-old's dismissal, slashing a Shaminda Eranga delivery to his counterpart Mahela Jayawardene in the slips, broke his perfect record of scoring at least a double-century once he surpassed 100 in 2012.
It also sparked a mini-collapse as Watson (83) and Matthew Wade (1) fell in quick succession to ill-conceived hook-shots, both caught in the deep before tea.
Watson's half-century was his first in eight innings and a welcome return to form, but the barrel-chested all-rounder will rue another lost chance to score his third Test century.
Watson had more bad news in store for him when Cricket Australia said in a statement late on Thursday that he had suffered a left calf injury while bowling on the first day of the match.
"He was able to get though the batting innings today and is likely to field on day three," physiotherapist Alex Kountouris explained.
"Whether he bowls in the second innings will be determined closer to the bowling innings."
The quick wickets gave Sri Lanka faint hope of saving the match but they were plunged back into the mire with a defiant seventh wicket stand of 61 from middle order batsman Mike Hussey and Johnson.
Hussey was caught for 34 shortly before the drinks break, with a mis-timed slog to long on off the bowling of part-time spinner Tillakaratne Dilshan.
Pint-sized spinner Rangana Herath put in a bid for catch-of-the-year as he scampered to his left and plucked an extraordinary, lunging catch with the thumb and forefinger on his left hand to draw kowtows from the crowd.
Johnson, who led Australia's first innings bowling with a four-wicket haul, marched on with seamer Peter Siddle and raised his seventh half-century with a push to mid-on for two.
Siddle was removed for 13 with a blinding catch to Jayawardene in the slips to give Eranga a second wicket.
It was again a day of lost opportunities for Sri Lanka, however, who dropped both Clarke and Watson late on day two.
Replacement wicketkeeper Kumar Sangakkara missed a stumping chance with Clarke on 54, while Mahela Jayawardene granted the Australian captain another reprieve on 83 by missing a catching chance in the slips off the bowling of spinner Rangana Herath.
Watson also had another life before lunch when the Sri Lankan captain spilled a sharp chance in the slips from the same bowler.
Mike Hussey was later dropped on seven by Sangakkara, who was standing in for Prasanna Jayawardene, the regular wicketkeeper having suffered a broken thumb when struck by a ball from Johnson on day one.
Sri Lanka batting coach Marvan Atapattu said Welegedera was in serious doubt to play the Sydney Test which begins January 3, but Jayawardene would "hopefully" bat at number seven again in the second innings.
"It's a long way from ending this game and we still have to have a good batting innings from the time we hopefully get them out in tomorrow's first session and see what we can do from there," he said.