Dobson had a 100% success rate with four penalties and a drop goal
Hull Kingston Rovers booked their place in the Challenge Cup quarter-finals in July with an ultimately comfortable win over Salford at The Willows.
A tight contest was scoreless until Blake Green crossed for Rovers' first try three minutes before the break.
Ben Cockayne added try number two three minutes after the restart before Kris Welham crossed too.
Jake Webster scored the fourth, Michael Dobson making it four kicks out of four, to add to his late drop goal.
Salford had the psychological advantage, having beaten Rovers 34-18 in Super League action in March.
And Rovers were put under pressure for long spells by a Salford side still in the caretaker charge of Phil Veivers, the former assistant to departed head coach Shaun McRae.
But it was not until the 39th minute that Green scored the game's opening try.
And this time, once Justin Morgan's men had made that late first-half breakthrough, although the scoreline flattered them, there was no stopping Rovers as they wreaked revenge.
Although further scores from Cockayne and Welham were not decisive, it was only after a late Dobson drop goal that Rovers could relax before Webster added a fourth try.
POST-MATCH REACTION
Salford caretaker coach Phil Veivers:
"It was a very good arm wrestle in the first half. We had three or four good opportunities and, if we could have taken them, we might have been talking about a different result.
"6-0 down at half-time it was still anyone's game but we got done by the same play twice, so it was a sucker punch.
"We had enough opportunities to score some points and you have got give the opposition defence some credit. They scrambled very well."
Hull KR coach Justin Morgan:
"I only really enjoyed the last six minutes when the game was put to bed. Even at 12-0 up they could have got themselves back into the game.
"They are no mugs, Salford. They have beaten some good teams. They were missing some players but it was a really good cup tie.
"The first half was fierce. There were no tries apart from the one just before half-time. That naturally makes the game fast."
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