Rogers scored 158 with Smith striding off at the close with 129 to his name as Australia reached 337 for one and almost certainly batted England out of the Test in the space of 90 overs.
And Rogers, who has played many times at Lord’s for Middlesex, admitted scoring a Test hundred at the home of cricket was special.
“It’s going to be one of the proudest moments in my career I think,” he told Sky Sports.
“To score a hundred at MCG then the SCG and then to get one here, it’s so special.
“I have a lot of support here, a lot of friends and it just feels amazing to do it.”
Smith was also pleased to reach three figures after coming in for criticism from some quarters despite his ranking as the world’s No 1 batsman.
His unorthodox technique has come under scrutiny but he well and truly silenced the doubters yesterday as he and Rogers put on 259 and counting for the second wicket.
“I was disappointed to miss out last game,” he said. “I felt quite good at the crease so I was disappointed with the way I played.
“I haven’t done so well here at Lord’s in the past so I wanted to make it count today and get myself up on that board and it’s really exciting to have done that today.”
Smith also admitted it was important to make a statement after the first Test defeat, and added: “It looks a pretty good wicket, well it did this morning when we first got out there, it was a little bit slow and it was one of those wickets where if you got in you needed to go big, that was what we said before the game.
“The way we’ve batted and put on 250 (as a partnership), good day.”
England seamer James Anderson refused to concede that the Test could not still be won despite Australia being on track for a colossal first-innings total.
“There’s four days left in the game. If we win four days, we win the Test match, so we’ve got to keep looking at it positively,” he said.
“We’ve still got a reasonably new ball in our hands in the morning. You never know, a bit of cloud cover might help us with a bit of swing.”
England, though, appeared set for plenty more toil at Lord’s after yesterday’s Australian run fest.
Michael Clarke won the toss on a cloudy morning, and unsurprisingly chose to bat first on a surface which looked flat and turned out to be just that.
David Warner’s wicket was England’s sole success in the first two sessions, the only other clear-cut chance coming when Smith edged Ben Stokes low to second slip on 50, Ian Bell failing to hold on. After their 169-run defeat in Cardiff, despite the loss of Warner to a moment of misadventure, the tourists soon took control of events here.
Warner began cautiously but then, after a rush of boundaries off first-change Mark Wood and Moeen Ali, he fell to the last ball of the off-spinner’s first over.
Wood was dispatched for 24 in three overs and 10 runs – including successive leg-side fours from the first two deliveries – had already been taken off and replaced by Moeen when Warner got greedy, went up the wicket and skewed his shot to deep and wide mid-off where Anderson took a fine, running catch.
Rogers had some initial moments of discomfort in defence against Anderson and Stuart Broad with the new ball, but, thereafter, he was increasingly composed.
One inside-edge past Rogers’ stumps off Wood on 64, and one off the outside of the bat from Smith past second slip for four off Stokes, were rare, and not especially compelling, signs that a wicket might be in the offing. On a pitch of little pace and entirely even bounce, the dominance of bat over ball was utterly routine.