At stumps, Australia were 337 for one after cashing in on captain Michael Clarke's good fortune in winning the toss and batting first on a placid pitch.
Rogers was a Test-best 158 not out at the close and Smith, dropped on 50, unbeaten on 129.
Their partnership was so far worth 259 runs and broke the previous Australia second-wicket record at Lord's of 231 set by Bill Woodfull and Don Bradman which had stood since 1930.
England's lone success in 90 overs' of toil was when off-spinner Moeen Ali had David Warner (38) caught in the covers by James Anderson shortly after the first hour's play.
Not since Geoff Marsh (125 not out) and Mark Taylor (141 not out) took their side to 301 without loss against England on the first day of the fifth Test at Trent Bridge in 1989 had Australia produced such a commanding display with the bat on the opening day of an Ashes match.
It was just the response the Ashes-holders, looking to win their first Test series in Britain in 14 years, would have wanted following England's 169-run win in the first Test in Cardiff last week.
Left-hander Rogers -- who plans to retire after this series -- knows 'the home of cricket' well from his time with Lord's-based county side Middlesex.
This was the 37-year-old's eighth fifty in nine Test innings but the first one in that sequence he had converted into a hundred.
Rogers batted the whole day as he spent more than six hours at the crease and in the process scored his fifth hundred in 22 Tests.
It was his highest score at this level, comfortably topping his 119 against England at Sydney in 2014.
"That's probably a little bit better to bat on than a usual Lord's pitch," Rogers told Sky Sports after both he and Smith gained a place on the Lord's honours board.
"It's one of the proudest moments of my career. To get a hundred here is so special."
Smith said: "That was very important after Cardiff.
"We said we needed to be more patient. Today was more about waiting for the bad ball and putting it away -- I wanted to make it count and get up on that board."
Initially overcast skies offered a hint of swing movement but long before tea the sun had broken through as conditions for batting eased.
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