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Australia captain Clarke raised his third consecutive half-century and became his country's highest test run-scorer in a calendar year, surpassing Ricky Ponting's 1,544 runs in 2005.
Clarke was on 56 and Watson on 60 as the pair added 88 runs in the morning to drive Australia's total to 238-3 on another day of brilliant sunshine at the Melbourne Cricket Ground.
Sri Lanka, skittled for 156 on day one, face a long day in the field, with the drop-in pitch drying out in hot northerly winds and with seamer Chanaka Welegedera off the ground injured after straining a hamstring.
Clarke and Watson resumed with the score 150-3 and negotiated a watchful opening phase of play before gradually hitting out before the drinks break. The pair had built a 121-run partnership from 270 balls by the interval.
Clarke, the year's leading run-scorer in tests, smacked a straight drive that slammed straight into Shaminda Eranga's foot, leaving the paceman hopping and grimacing in pain down the pitch.
Eranga exacted a modicum of revenge a few overs later, hitting Clarke on the helmet with a mean short delivery, but undid some of his menace in the same over with a careless throw at the stumps that went straight to the boundary.
Watson's half-century was his first in eight innings, and a welcome return to form after struggling to capitalise on a number of starts.
The barrel-chested all-rounder smashed an imperious straight six off spinner Rangana Herath that hit the sightscreen on the full at the northern end.
Clarke's milestone, acknowledged with a wave of a bat at the crowd and the dressing room, put him in fifth place for most runs in a calendar year, but a big score in Melbourne could see him move up another couple of places.
Pakistan's Mohammad Yousuf holds the record of 1,788 runs scored in 11 tests in 2006.