Leeds United, producing a performance many Elland Road regulars reckoned to be among the best of recent times, were simply too good in all departments for Rovers. Way too good.
The final scoreline barely told half the story of the home team's dominance. Leeds scored three goals, hit the woodwork five times and goalkeeper Luke Daniels made half a dozen outstanding saves.
Rovers manager John Barnes admitted his team could have lost by six or seven. It could have been even worse than that.
The pass-and-move football Barnes wants his team to play was scarcely in evidence because Leeds dominated possession and made all the best moves.
They were sharper, stronger and hungrier for the ball, hustling Tranmere out of possession. They attacked with pace and invention that opened gaping holes in the visitors' defence.
Jermaine Beckford scored one goal and could have finished the afternoon with a couple of hat-tricks.
Striking partner Luciano Becchio scored the third goal late on, a fitting reward for the Argentine's efforts in running the defenders ragged.
Midfielder Robert Snodgrass tormented Tranmere with his probing runs and crosses from the right and Bradley Johnson, the scorer of the opening goal, was scarcely less effective on the opposite flank.
Meanwhile, skipper Jonathan Howson directed the one-way traffic from central midfield.
It takes a club with Leeds' strength of support and spending power, exceptional at League One level, to afford players of such calibre. On this evidence they deserve to be regarded as promotion favourites.
Manager Simon Grayson enjoyed watching their football so much he "felt like a fan at times."
He added: "Performances like that don't happen overnight. The quality we had in possession was outstanding in the chances we created were down to the work-rate throughout the team."
As much as Leeds' football was irresistible, the visitors did not resist effectively enough.
Tranmere's resources are meagre in comparison to those of Leeds and Barnes is working on a budget cut back even on last season's modest levels.
Even so, Rovers were more competitive than this in four previous League One meetings with Leeds over the last couple of years.
The contrast in spending power certainly wasn't an excuse Barnes raised in the post-match Press conference, arguing that Tranmere allowed Leeds to look so good.
Barnes said the dressing room game-plan was to subdue the 20,000-plus home crowd during the opening 15 minutes by keeping possession as much as possible.
But within a minute of the kick-off a defensive lapse allowed Beckford to chase clear through the middle and drive a shot against the feet of the advancing Daniels.
Four minutes later Beckford, making a diagonal run through a disoriented Tranmere rearguard, rifled a shot against the inside of the left-hand post.
The genie was out of the bottle and Tranmere could not find a way to put it back in again.
Tranmere came no closer to a goal all afternoon than in the 25th minute when a long clearance from Daniels was nodded on by Craig Curran towards striking partner Ian Thomas-Moore, whose attempt to hook the ball home from six yards was thwarted by a fine tackle from Patrick Kisnorbo.
It was nothing more than a brief respite from the wave of penetrating Leeds attacks.
Daniels went full stretch to keep out a low 20-yarder from Beckford. But then on 35 minutes a long ball from the back by a Andrew Hughes glanced off the head of Ian Goodison and dropped to the feet of Beckford to steer home from close range.
Soon afterwards, Rovers had to withdraw centre back Gavin Gunning because of a problem with blisters. Replacement Ash Taylor found the going just as difficult.
Daniels had to make another full-length save from Johnson just before the interval and the urgency of Leeds football on the resumption suggested Grayson insisted on no let-up in the pressure.
Beckford, running on a Snodgrass through pass on 54 minutes, chipped his shot against the crossbar.
Daniels made the best of his saves by keeping a deflected 25-yard volley from Kisnorbo out of the top corner.
He was beaten by Beckford's venomous 30-yard effort on 64 minutes but the ball crashed high against the left-hand post.
Another Daniels save, this time from Johnson's 25-yard shot was followed by another brush with the woodwork as defender Rui Marques nudged a Snodgrass corner against the post.
More than half of Tranmere's supporters had left the stadium by the time Leeds scored the third on 86 minutes when Becchio nodded home after a free-kick from Johnson bounced back off the crossbar.
Thanks to Nick Hilton, Liverpool Daily Post for the above match report.