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After a lively start, United took the lead in the 18th minute with the Tranmere defence all at sea after Eugen Bopp's cross caused havoc.
The ball arrived at the feet of star midfielder Lee Williamson and he found space to fire home a fierce angled shot for his first goal of the season.
Good work by Chris Greenacre and Gareth Taylor set up Kevin Ellison and he coolly steered home a precision shot to bring Rovers level with his second of the season.
Undeterred, the Millers pressed forward and hot-shot Will Hoskins put them back in front with an excellent low shot after cutting inside the Rovers defence on 38 minutes.
The pressure continued with Taylor and Ellison seeing goalbound efforts cleared after a strong spell of pressure shortly before the break.
The second half was a stop-start affair with the Millers defence relatively untroubled against an impotent Rovers forward line with ex-United men John Mullin, Robbie Stockdale and Paul McLaren not enjoying their first return to the club.
Gregor Robertson and Hoskins spurned chances to steal the win for the hosts with Rovers' only worthwhile chance seeing sub Calvin Zola steering an effort off target.