Iraola's first Liverpool team featured Joe Gomez wearing the captain's armband, though his involvement lasted barely 10 minutes before he was forced off with a knock, replaced by Ifeanyi Ndukwe as Kostas Tsimikas took over the captaincy.
Kieran Morrison put the Reds ahead on 12 minutes, cutting inside from the right after being slid in by Harvey Elliott and finishing low into the bottom corner, only for Enzo Le Fee to level for Sunderland shortly after with a powerful drive from just inside the box.
Sunderland went close to taking the lead through Romaine Mundle, with Giorgi Mamardashvili parrying his effort before James McConnell blocked Chris Rigg's follow-up, and the sides went in level at 1-1 at half-time.
Iraola made five changes at the break, but it was the Black Cats who struck first in the second half, Timur Tutierov hooking home from close range four minutes after the restart following a nudged pass from Tom Proctor.
Liverpool responded emphatically. Dominik Szoboszlai levelled on 56 minutes with a crisp half-volley after controlling a loose ball on his chest just outside the box, before Federico Chiesa put the Reds ahead for the first time since the opening goal, finishing off a pass from Calvin Ramsay with an angled effort from the corner of the six-yard box.
Lewis Koumas completed the scoring with four minutes remaining, collecting a Szoboszlai pass and cutting inside Leo Hjelde before finishing from 10 yards, sealing a fourth pre-season friendly win in some style for Iraola's side.
The result gives Iraola an encouraging start to life at Anfield ahead of a summer schedule that will continue to test his squad's depth, with a crowd of 24,897 turning out at GEODIS Park to watch the Spaniard's first match in charge.
Liverpool's ability to fight back from behind twice, including once in each half, will offer particular encouragement as pre-season preparations continue.
Liverpool: Mamardashvili (Woodman 67), Gomez (Ndukwe 8), Jones (Nyoni 46), Elliott (Szoboszlai 46), Tsimikas (Kerkez 46), Frimpong (Ramsay 67), McConnell (Scanlon 56), Morrison (Abe 67), Ngumoha (Koumas 46), N'Diaye (Chambers 67), Wright (Chiesa 46). Unused subs: Davies, Sonni-Lambie.