Huddersfield midfielder Adnan Ahmed was sent off in the 58th minute for a challenge described by his own manager, Peter Jackson, as "horrific".
Ahmed hacked down big striker Mark McCammon and Huddersfield striker Pawel Abbott was also dismissed for lashing out in the ensuing melee.
Rovers left-back Gareth Roberts saw red following a two-footed challenge on Aaron Hardy in a separate incident nine minutes from time.
But Doncaster already had the game sewn up before the rash of red cards, with McCammon having the honour of becoming the first player to score a goal at the new Keepmoat Stadium.
He latched on to a long kick from keeper Ben Smith to volley home in fine style in the ninth minute.
Doncaster always had the upper hand, but lived dangerously at times as Huddersfield managed to carved out chances, but proved woefully weak in front of goal.
Visiting keeper Matt Glennon had already done well to tip a cracking effort from Paul Heffernan before McCammon struck.
But Abbott fired wide after latching on to a clearance from Danny Adams in the sixth minute and Michael Collins missed a great chance to equalise when he fired wide with only the keeper to beat in the 24th minute.
Glennon did well to parry shots from Paul Heffernan and Jonathan Forte as Rovers piled on the pressure, roared on by a 14,470 crowd - their biggest home gate for over 20 years.
Heffernan made it 2-0 early in the second half after Forte had put him in the clear and the Rovers top scorer produced a clinical finish to notch his 11th of the season.
The game was as good as over in the 51st minute when Forte rounded off a fine move involving Heffernan and James Coppinger to rifle home the third goal into the top corner.
The game was then marred by the series of dismissals and Doncaster decided to hold on to what they had by just passing the ball around in the closing stages.
Substitute Bruce Dyer had a low effort saved in injury time as the Rovers fans began celebrating their start to the New Year.