Raducanu overcame injury doubts and illness to beat Danka Kovinic in her opener at Indian Wells, and the British No 1 had to call for a physio after battling back from an early deficit.
Poland’s Linette, 21st in the WTA rankings and 55 places higher than Raducanu, took the first break of the match for a 3-1 first-set lead.
But Raducanu fought back from 4-1 down to level at 4-4 before calling for a physio at 6-5 ahead.
Both players, somewhat bizarrely, lost their serve to love as the opening set went into overtime.
Raducanu, who beat Linette in their only previous meeting at the 2022 Korea Open, won the tie-break 7-3 to establish an advantage after 62 minutes on court.
The odds were really stacked against Linette when Raducanu broke serve to lead 3-1 in the second set.
— LTA (@the_LTA) March 11, 2023
She comfortably closed out victory against this year’s Australian Open semi-finalist and will now meet either Katerina Siniakova of the Czech Republic or Brazil’s Beatriz Haddad Maia in the last 32.
It was a big win for Draper, 27 spots below the 29th-placed Evans on the ATP rankings and marks an upturn in his fortunes after illness and fitness issues in recent months.