Under pressure following his poor form all series with the bat, Watson smashed 25 fours and a six to reach 176, from 247 balls, at The Oval.
"It's definitely a relief to be able to make a hundred, there's no doubt about that," Watson said. "But it was important to be able to bat for a longer period of time in an Ashes test. I've not read one thing (of criticism). I know the thing is that if I'm not performing I'd expect people to write things that are not complimentary, but I've stayed away from it.
"I'm very critical of myself anyway so I don't read anything that would compound it."
Watson batted on after taking a fierce blow to the head from a bouncer by Stuart Broad, was dropped on 104 by Alastair Cook in the slips and overturned an lbw decision to Chris Woakes on 160, before he finally fell to Broad.
Steve Smith was unbeaten on 66 (nine fours, one six 133 balls) as England's bowlers struggled, James Anderson finishing with the best figures of 2-52.
"It was a long day for us," Anderson said. "We stuck to our task pretty well as a bowling unit. It was a pretty lifeless pitch and I though Watson played out of his skin."
Australia won the toss and chose to bat but had to endure a hostile opening spell from Anderson and Broad before Watson hit debutants Woakes and Simon Kerrigan out of the attack.
Warner lasted only 18 minutes before getting an outside edge to Anderson for wicketkeeper Matt Prior to accept the catch.
However, England's decision to release fast bowlers Steven Finn and Chris Tremlett from its squad and go without experienced backup for the opening quicks backfired when Watson gave the new boys a harsh introduction to test cricket.
Watson hit both Woakes and Kerrigan for six fours, but he also smashed Graeme Swann for a six over the sightscreen and brought up his 50 from 61 deliveries when he nudged a single from Kerrigan.
Australia reached 100 when Watson hit Kerrigan for 18 in the 25th over, forcing England captain Alastair Cook to bring back Broad in a bid to stem the flow of boundaries.
Broad responded with a maiden over, but the century partnership was reached in the final over before lunch when Rogers flicked Broad for three runs through midwicket.
Rogers fell for 23 early in the afternoon session when he edged Swann to Jonathan Trott, who took a low catch at first slip.
Watson was on 91 when he was hit on the back of the head by a Broad bouncer. The blow struck the batsman just below the helmet, but after a two-minute delay he continued.
"I was pretty lucky really," Watson said. "It got me in a good spot, in the muscles. It certainly got me thinking there was more to worry about than being in the nervous nineties."
Michael Clarke looked vulnerable throughout his 39-ball innings and was bowled off his pads by Anderson in the 43rd over. In the next over, Watson, having slowed slightly since lunch, reached his first century in 48 attempts with a stroke for three from Anderson.
England then squandered the momentum when Cook dropped Watson after he edged Anderson to first slip.
The debutants returned at the end of the session. Woakes improved significantly, but Kerrigan's final over before tea began with a rank, head-high full toss that Smith swatted for four.
Anderson acknowledged that Kerrigan had suffered.
"The guys in the dressing room have got a job to do to rally around him and keep his spirits high," he said. "He's had a bad day but the other days know what he can do, he's a quality bowler."
Watson was diplomatic about Kerrigan's performance, but said he was surprised by England's selections.
"I was expecting Tremlett to play," he said. "He's had quite a lot of success bowling against us. I was a lot happier than I would have been if I'd had to face a guy who's 6'8 and bowling balls up into your face."
In an evening session short on drama, Watson reached his 150 when he flicked Broad to the fine leg boundary and Smith drove Swann for a single to pass 50.
Watson was given out lbw to Woakes in the 82nd over but he referred the call and the decision was reversed — only the second time Watson has overturned an lbw call in nine attempts.
Watson's luck finally ran out in the 88th over when he holed out to Broad and fell to a brilliant tumbling catch by Kevin Pietersen, although only after an umpire referral for a no ball confirmed Broad's foot was fractionally behind the crease.
Australia sent in Peter Siddle as nightwatchman and he added an assured 18 not out before stumps.