Muriel took Udinese's first and practically only chance of the game 10 minutes before the interval to earn all three points, which have edged them up towards the European qualifying berths in Serie A as a result.
Siena had chances to get something out of the game, but Alessandro Rosina missed their best ones, summing up their season so far with the ball seemingly not wanting to go in.
Udinese took a negative approach to the game, leaving Antonio Di Natale and Muriel alone up front and inviting Siena to attack them.
The Tuscans were happy to oblige, but for all their efforts they struggled to create any clear-cut openings.
Their best chance arrived in the 27th minute when Rosina received the ball near the penalty spot with only Daniele Padelli to beat, but he shot straight at the Udinese goalkeeper.
When the home team finally saw the occasion to break, they seized it to take the lead in the 36th minute.
Di Natale stole possession in midfield and fed Allan, who touched the ball on for Muriel to place it in low past Gianluca Pegolo.
It as the epitome of efficiency from the home side, who took their one and only chance of the half to go into the break ahead.
Rosina then missed a glorious chance to level matters just 34 seconds into the second half when he failed to make contact with the ball just six yards out when, again, he only had Padelli to beat.
Siena tamely tried to find a way back into the game while Udinese continued to look happy just sitting on their lead, which they managed to do without breaking a sweat.