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World No 1 Djokovic said he was pleased to have passed a huge test on his injured right ankle following a 4-6, 6-1, 6-4 defeat of Russian Mikhail Youzhny.
Djokovic admitted that at one point in the second set he felt some pain but played through it successfully, thanks in part to his heavy strappings.
VIDEO: Nadal v Matosevic, highlights
Second seed Murray posted an uneventful 6-1, 6-4 win over Frenchman Eduardo Roger-Vasselin while Nadal began his favourite part of the year and a quest for a ninth straight title here with a 6-1, 6-2 defeat of Marinko Matosevic.
Djokovic had waited until the last minute to make his decision on whether he could compete, having rolled his ankle on Davis Cup duty 10 days ago. He earned a late break for 5-4 in the final set as Youzhny missed a drop shot, before serving out the match.
"I think that my ankle is in a good state as the days are passing by," said the winner. "Today was a big test, I had a great quality opponent.
"My clay movements are still not at the maximum. But I'm going to slowly get into it. Hopefully I can elevate the level of performance in the next match.
"I'm very happy to win, I'm just happy to compete, to be honest. I didn't know if I'm going to be playing the tournament up to yesterday (Tuesday) basically."
Murray was pleased with his own effort on his weakest surface as he beat Roger-Vasselin.
"It’s always difficult to move when you get to this surface. I started the match well and he made a lot of errors in the first set. I was able to take advantage of them."
Nadal was totally in his comfort zone on another sunny, warm day on the Mediterranean, demolishing the Australian in 62 minutes.
"I played well with the right feelings and doing the right things, so I'm very happy," he said. "I had the right intensity, with no mistakes.
"I was trying to find a good feeling on the ball, to find the right rhythm. And I think I did, no? That gives me confidence."
Nadal's quick win marked a successful return to action after resting for three weeks in the wake of his Indian Wells title of last month.
The 26-year-old is planning his schedule more carefully after missing seven months of play in 2012-2013 due to his chronic knee problems.
But he will have little rest in the run-up to Roland Garros, with entries set for Barcelona plus the Madrid and Rome Masters over the next four weeks.
Nadal, playing Monte Carlo for the 10th time, improved his phenomenal record here to 45-1, with his only loss coming to Guillermo Coria in 2003 as a teenager.
He said, though, that despite his enviable Monte Carlo run, he feels no extra pressure to win.
"I feel that I am coming here trying to play well. As in every tournament, (I) try my best in every moment.
"If that happens, if I'm able to play my best tennis, probably I will have my chance to be in a good position to play in the last rounds, to fight for important things."
Nadal next plays German Philipp Kohlschreiber.
Elsewhere in the second round, Czech fourth seed Tomas Berdych began his clay season with a defeat of Spain's Marcel Granollers 7-5, 6-4.
Croatian ninth seed Marin Cilic put out South African Kevin Anderson 6-2, 6-3, while Austrian Jurgen Melzer upset Spanish tenth seed Nicolas Almagro 6-4, 6-2 and veteran Finn Jarkko Nieminen upset Canadian 12th seed Milos Raonic 6-3, 1-6, 7-6 (7/3).
Second round
Jarkko Nieminen (FIN) bt Milos Raonic (CAN x12) 6-3, 1-6, 7-6 (7/3)
Tomas Berdych (CZE x4) bt Marcel Granollers (ESP) 7-5, 6-4
Rafael Nadal (ESP x3) bt Marinko Matosevic (AUS) 6-1, 6-2
Marin Cilic (CRO x9) bt Kevin Anderson (RSA) 6-2, 6-3
Florian Mayer (GER) bt Roberto Bautista Agut (ESP) 5-7, 6-4, 6-4
Jurgen Melzer (AUT) bt Nicolas Almagro (ESP x10) 6-4, 6-2
Stanislas Wawrinka (SUI x13) bt Albert Montanes (ESP) 6-1, 6-1
Fabio Fognini (ITA) bt Albert Ramos (ESP) 6-3, 7-5
Novak Djokovic (SRB x1) bt Mikhail Youzhny (RUS) 4-6, 6-1, 6-4
Andy Murray (GBR x2) bt Eduardo Roger-Vasselin (FRA) 6-1, 6-4
Juan Monaco (ARG x14) bt Ernests Gulbis (LAT) 6-0, 3-6, 6-3
