In a poor first half, the Welshman's coolly-taken penalty was enough to separate the sides at the break.
However, the second period was a different story, with another well-taken goal from Robson-Kanu, one from super-sub Adam Le Fondre and Jem Karacan's drilled strike cancelling out a Bryan Ruiz double for the hosts, and sealing the points for the Royals.
The result was Nigel Adkins' first win as Royals boss, and gives them a sense of pride before they begin to plan for life in the Championship, whilst Fulham have now lost four in a row as their season disappointingly peters out.
The home side almost broke the deadlock within the first minute, as Ruiz did well to get on the end of a floated Damien Duff cross, but Alex McCarthy continued his heroics in the Reading goal, blocking well at his feet.
And that save proved vital as Robson-Kanu coolly scored from the spot after Riise had fouled the Welshman just inside the box.
The visitors were on top for the majority of the first half after that, with Fulham fans voicing their frustration at the wayward passing of their side.
After the interval it was end-to-end stuff and poor defending from the home side allowed Robson-Kanu to double his and Reading's tally with a precise curler past Mark Schwarzer.
Ruiz then played a neat one-two with Hugo Rodallega on the edge of the Reading box, with the Costa Rican finishing well after collecting the return pass.
However, as quickly as the Craven Cottage faithful had got their hopes up, they were soon dashed as, moments after coming on, Le Fondre rounded Schwarzer and slotted in the Royals' third.
Minutes later, Ruiz again was on the scoresheet, nodding in Alex Kacaniklic's cross when unmarked on the penalty spot to put Fulham back in it.
But once again, poor defending dashed the home support's hopes, as Karacan was first to react to Brede Hangeland's clearing header to put the game beyond the Cottagers' reach.
Fulham had several late chances, with Rodallega coming close on three occasions, but it was not to be as Martin Jol's men continued their below-par end to the season, and Reading enjoyed the taste of a rare three points on the road.