Meanwhile, Novak Djokovic continued his clay court-season resurgence with another straight-sets win at the French Open, defeating Jaume Munar 7-6 (7-1), 6-4, 6-4.
In another men's singles match, Grigor Dimitrov of Bulgaria defeated Jared Donaldson 6-7(7-5), 6-4, 4-6, 6-4, 10-8 in a thrilling five-setter that lasted 4 hours, 19 minutes.
The former world number one has admitted motivation has been an issue during a tough spell in which form and fitness have deserted him - last winning an ATP Tour title at Eastbourne in July - but he pushed clay king Rafael Nadal hard last time out in the Internazionali d'Italia final.
And Djokovic has started well at Roland Garros, following up Monday's triumph over Rogerio Dutra Silva with a hard-fought victory on Court Suzanne Lenglen.
Recovering from slump
Halep, the runner-up in Paris in 2014 and 2017, slumped 0-5 down in the opening set to world number 83 Riske whose only win at the tournament came in 2014. The Romanian committed 16 unforced errors in the set but stepped up a gear from that point on to book a second-round match against Taylor Townsend of the United States.
Off to a flying start!
Alison Riske puts Halep on upset alert taking the first set 6-2.#RG18 pic.twitter.com/EBbdIhFSoI — Roland-Garros (@rolandgarros) May 30, 2018
"It's always difficult in the first round of a Grand Slam, you are always nervous," said Halep whose opening round match had been cancelled on Tuesday due to torrential rain.
Malgré un faux départ dans le 1er set, Simona Halep passe l'obstacle américain Alison Riske 2-6 6-1 6-1#RG18 pic.twitter.com/1VPgchFELb — Roland-Garros (@rolandgarros) May 30, 2018
"But I started to run more, played better and kept more balls in play." Halep needs to reach the semi-finals or better if she is to retain the world top spot.
The two-time Wimbledon champion, Kvitova, has now won 13 consecutive matches on clay after claiming titles in Prague and Madrid and will face either Romanian Alexandra Dulgheru or Estonia's 25th seed Anett Kontaveit for a place in the last 16.
Lucky #️⃣1️⃣3️⃣@Petra_Kvitova notches her 13th consecutive match win, blasting past Arruabarrena 6-0 6-4 to book her spot in the 3R.#RG18 pic.twitter.com/fAMEeK0IWY — Roland-Garros (@rolandgarros) May 30, 2018
Czech Kvitova has not reached the quarter-finals at Roland Garros since a run to the last four in 2012.
The 28-year-old raced through the opening set in only 24 minutes, and although she was pegged back after an early break in the second, a booming forehand sealed a victory with a third straight game.
In other men's singles action, Alexander Zverev was far from his best but was still able to battle past Dusan Lajovic in a five-set thriller.
Zverev has been one of the in-form players on clay this year with 17 wins and two titles to his name on the red dirt - including victory over Dominic Thiem at the Madrid Open.
He eased past Ricardas Berankis in the opening round in Paris but Lajovic proved a much tougher test, Zverev eventually progressing 2-6, 7-5, 4-6, 6-1, 6-2.
A relieved Zverev will play Damir Dzumhur in round three as he looks to go further than ever before at Roland Garros - although he can ill afford the mistakes that delayed his latest victory.
Kei Nishikori of Japan ended the hopes of Frenchman Benoit Paire 6-3, 2-6, 4-6, 6-2, 6-3.
STATISTICAL BREAKDOWN Djokovic bt Munar 7-6 (7-1), 6-4, 6-4
WINNERS/UNFORCED ERRORS Djokovic - 39/33 Munar - 28/23
ACES/DOUBLE FAULTS Djokovic - 3/5 Munar - 3/3
BREAK POINTS WON Djokovic - 5/7 Munar - 3/7
FIRST SERVE PERCENTAGE Djokovic - 69 Munar - 61
PERCENTAGE OF POINTS WON ON FIRST/SECOND SERVE Djokovic - 71/60 Munar - 65/44
TOTAL POINTS Djokovic - 107 Munar - 86
STATISTICAL BREAKDOWN Zverev bt Lajovic 2-6, 7-5, 4-6, 6-1, 6-2
WINNERS/UNFORCED ERRORS Zverev - 42/53 Lajovic - 38/61
ACES/DOUBLE FAULTS Zverev - 9/7 Lajovic - 0/4
BREAK POINTS WON Zverev - 7/23 Lajovic - 5/10
FIRST SERVE PERCENTAGE Zverev - 57 Lajovic - 57
PERCENTAGE OF POINTS WON ON FIRST/SECOND SERVE Zverev - 77/46 Lajovic - 67/43
TOTAL POINTS Zverev - 156 Lajovic - 141
(Additional inputs by OPTA)