Seven-time champion Nadal - seeking to reclaim the number-one ranking he conceded last week - hammered Dzumhur 6-1 6-0 after Thiem had gone down in three sets to Fabio Fognini, the Austrian smashing a racquet in anger during an intense contest.
Alexander Zverev got his Rome title defence underway at the Italian Open on Wednesday with a straight-sets win over Italy's Matteo Berrettini as the German bids for back-to-back Masters triumphs after success in Madrid.
The 31-year-old, whose 21-match unbeaten run on clay ended last week, had a first-round bye and will play Denis Shapovalov or Robin Haase next.
Rafael Nadal swept aside Damir Dzumhur 6-1, 6-0, while in the women's draw, top seed Simona Halep beat Naomi Osaka by the same scoreline.
"I played very well today", said Thiem.
The 16-time Grand Slam victor next takes on either Canadian Denis Shapovalov, 19, or Robin Haase of the Netherlands.
Djokovic was up against Georgia's Nikoloz Basilashvili and settled down after a nervy start to wrap up a 6-4, 6-2 victory after one hour and 18 minutes.
Djokovic, a four-time victor of the Italian Open, also had little trouble in his second round match, defeating Georgia's Nikoloz Basilashvili 6-4, 6-2 in one hour and 18 minutes.
Djokovic, meanwhile, has now secured convincing back-to-back wins in Rome as the Serbian continues to feel his way back after the elbow injury that kept him sidelined for half of last season and prolonged spells this year.
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Following a shot that Thiem sent far and wide past Fognini's baseline, the former was so incensed that he swung his racquet to the ground, and clearly one swing wasn't enough as he continued to destroy it on the clay.
"I went on court with the right intensity".
After the match, Pliskova didn't shake hands with the chair umpire and struck the chair several times with her racket.
Halep needed to save four break points in her opening service game for 1-1 but then reeled off 12 in a row.
Halep reached the final in Rome previous year and needs to reach the quarter-finals this time to retain her world number one ranking.
On Halep's first match point, the 21st-ranked Osaka didn't even make a move for Halep's return of her second serve.
Maria Sakkari of Greece rallied past sixth-seeded Karolina Pliskova 3-6, 6-3, 7-5.
Also, U.S. Open champion Sloane Stephens held off a comeback from Estonian qualifier Kaia Kanepi in a 6-0, 5-7, 6-4 victory; seventh-seeded Caroline Garcia defeated Timea Babos 6-3, 6-4; and 14th-seeded Daria Kasatkina eliminated American qualifier Danielle Collins 6-2, 6-3. I don't know how many mistakes I made, but not many.