Reigning champion Halep was taken the distance in her opening two matches at Roland Garros but sailed through against Tsurenko, who appeared to be struggling with injury after requiring three hours and three minutes across two days to see off Aleksandra Krunic in the second round.
The Ukrainian struggled behind her serve and just two holds for Halep — something that may rankle despite the relatively routine win — proved sufficient for her to take the opener.
Tsurenko took a medical time-out after falling 3-0 down in the second set and the No.3 seed showed no mercy as she sealed the victory in confident fashion.
The Ukrainian twice double faulted on break point — she produced three in succession in her second service game — as Halep took a 3-1 lead in the opening set.
Tsurenko was also struggling with her groundstrokes and four straight unforced errors handed Halep another break.
Although Tsurenko hit straight back, she was quickly struggling again and Halep had the set wrapped up when the No.27 seed went long with a backhand slice.
The Romanian broke in the opening game of the second with a searing backhand down the line and took a 5-0 advantage after Tsurenko received treatment on a thigh issue.
Halep had sped through gears and, after being broken to love, completed a rapid triumph with a backhand volley at the net.
Simona Halep  bt Lesia Tsurenko  6-2 6-1
Halep - 9/14
Tsurenko - 8/32
Halep - 0/3
Tsurenko - 0/5
BREAK POINTS WON
Halep - 8/10
Tsurenko - 3/3
FIRST SERVE PERCENTAGE
Halep - 74
Tsurenko - 62
PERCENTAGE OF POINTS WON ON FIRST/SECOND SERVE
Halep - 61/33
Tsurenko - 41/5
Halep - 55
Tsurenko - 30