"It was odd, I must admit, playing Kei in the first round", Djokovic said.
"I think that Djokovic is one of those players".
"I'm glad that match went my way, but it could have gone his way as well".
Djokovic, last year's semi-finalist in Madrid and this year's and 10th seed, was attempting to get his season going after nursing a lingering right elbow injury.
The Joker has been eliminated before the quarter-finals of five tournaments already this year and also bowed out early in his last outing at the Monte Carlo Masters, after being defeated by Dominic Thiem in the third round. Schwartzman will next face Spaniard Feliciano Lopez, who beat countryman Pablo Andujar 7-6 (4), 6-3 on Monday, with a possible battle with top-seeded Rafael Nadal awaiting the victor in the Round of 16. She has been dealing with a left forearm injury.
Nishikori withdrew from his opening match in Barcelona last time out while Djokovic has found both form and fitness hard to come by. "In both first and second set I made breaks, you know, to win both sets at the really final stages of both sets". "That will certainly help me moving forward". Wozniacki reached the 2009 final on debut and hasn't been close since.
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Elsewhere on Monday in the clay-court event, 15th-seeded Frenchman Lucas Pouille fell to countryman Benoit Paire 6-2, 6-3, marking Pouille's fourth consecutive defeat in the first match of a tournament.
"I was lucky to get away with it in that third set", the second-seeded Wozniacki said.
The only other seeded player in action was 13th-seeded Argentinian Diego Schwartzman, who cruised past France's Adrian Mannarino 6-1, 6-3 in a little over an hour.
In a first-round match between Frenchmen, Benoit Paire hit 39 winners to defeat 18th-ranked Lucas Pouille 6-2, 6-3, advancing to face 19-year-old Denis Shapovalov of Canada, who got past Tennys Sandgren of the US 6-1, 6-4.
Dusan Lajovic, Federico Delbonis, Mikhail Kukushkin and Damir Dzumhur are also through.