The Finland international was on target in Celtic's 1-1 with Rapid Vienna on Sunday, and he continued that goalscoring trend on Tuesday.
Pukki twice cancelled out goals from Linz in each half, before putting Celtic ahead for the first time in the 64th minute.
Fellow strikers Amido Balde and Leigh Griffiths were also on target in a comfortable win for the Glasgow outfit.
Delia took the opportunity to run the rule over his squad with academy products Eoghan O’Connell, Stuart Findlay, Calum Waters, Liam Henderson, Bahrudin Atajic and Callum McGregor all featuring.
And Celtic's youthful side fell behind in the 21st minute when Radovan Vujanovic bundled home from a corner, only for Pukki to bag his first of the evening 11 minutes later.
Linz restored their lead just nine seconds after the restart with half-time substitute Tobias Pellegrini making an immediate impact.
However, the advantage was shortlived, Pukki finishing Adam Matthews' cut-back two minutes later, before his cultured finish put Celtic ahead in the 64th minute.
Balde added further gloss before Pukki was replaced 13 minutes from the end, and there was time for Griffiths to apply a predatory finish inside the area in the closing stages to complete the win.
Celtic have one more run-out against Dukla Praha on Friday before facing KR Reykjavik in the first leg of their UEFA Champions League second-round qualifier next Tuesday.