Burge fined Rutherford 50 per cent of his match fee under the International Cricket Council's code of conduct for attempting to intimidate one of the umpires and Ranatunga 25 percent of his fee for showing dissent at his dismissal.
Sri Lanka eventually won the match by five wickets to keep their hopes alive in the limited-overs competition.
In Rutherford's case, the Sri Lankan batsman Hashan Tillekeratne had played forward defensively and then had hit the ball a second time to prevent it from bouncing on to his wicket.
"Rutherford breached ICC code of conduct clause No 4 in that he attempted to intimidate an umpire into a favourable decision by moving towards the South African umpire Cyril Mitchley with hands raised shouting `that's out'," Burge said in a statement.
Rutherford said: "I got it wrong... I suggested to the umpires that it might be a case of hitting the ball twice or of obstructing the field. He said it wasn't. I realised that I was completely wrong, but a bit of gamesmanship here and there isn't unwarranted."
Ranatunga "showed obvious dissent to his being given out caught behind by indicating the ball came off his pad, shaking his head and commenting to the umpires that he did not hit it", Burge said.
Meanwhile, Waqar Younis took his first hat-trick for Pakistan yesterday as New Zealand were bowled out for a disappointing 172 in another of the Mandela Trophy matches at the same venue, Pakistan going on to record a comfortable five-wicket victory.
Waqar mopped up the final three wickets to finish with 4 for 33, New Zealand capitulating in 47.3 overs.Waqar ended the innings in fine fashion by bowling Chris Harris, Chris Pringle and Richard de Groen.
Only Blair Hartland, who put on 36 in nine overs for the first wicket with Bryan Young, and Rutherford were able to get among the runs. Hartland hit a confident 44 from 69 deliveries and Rutherford a fluent 30 off 46 balls. The pair put on 44 for the third wicket.
On a slow pitch where the occasional ball kept a little low, the Pakistan attack applied continual pressure by taking wickets at regular intervals.
MANDELA TROPHY (East London, South Africa): New Zealand 172 (47.3 overs, Waqar Younis 4-33); Pakistan 175-5 (38.5 overs). Pakistan win by 5 wickets.Reuse content