Atlanta cruised to a 4-0 rout of Herediano – inspired by Josef Martinez's brace at home to the Costa Rican visitors on Thursday – and 5-3 aggregate triumph.
De Boer's competitive bow had ended in a 3-1 loss away to Herediano last week but the former Crystal Palace and Inter boss – a replacement for championship winner and current Mexico boss Gerardo 'Tata' Martino – earned his maiden victory in charge.
Martinez, who was the leading goalscorer in MLS last season, broke the deadlock after just 47 seconds from the edge of the six-yard box.
Atlanta drew level on aggregate but moved ahead on away goals when Julian Gressel found the back of the net in the ninth minute.
Atlanta United FC (@ATLUTD) March 1, 2019
Venezuelan star Martinez netted his second with a 63rd-minute tap-in before Leandro Gonzalez Pirez sealed the triumph with seven minutes remaining.
Atlanta will face Mexican side Monterrey for a spot in the semi-finals of the Champions League.
Meanwhile, Sporting Kansas City defeated 10-man Toluca 2-0 for a 5-0 aggregate win and a quarter-final showdown against Independiente.
After cruising to a 3-0 first leg win at home, Sporting KC took to the road and faired just as well in the altitude against Toluca.
Sporting KC winger Gerso opened the scoring after just eight minutes, all but sealing the victory, before Krisztian Nemeth added a finish from the penalty spot in the 62nd minute.