Kilmarnock 0 Celtic 2: Deila's men move within a point of leaders
Ronny Deila's side had slipped off top spot after two games without a win, but they surged back into contention with a 13th victory of the league campaign.
Kris Commons shone for Celtic and could have opened the scoring on two occasions in the opening half hour, but the forward saw both efforts thud against the crossbar.
Izaguirre had no such problems, though, as he raced forward from full-back to collect a Stefan Johansen pass and volley past Craig Samson with nine minutes of the half remaining.
Commons continued to pull the strings in the second half and was denied for a third time as Mark Connolly produced a last-ditch tackle.
Celtic's second goal eventually arrived after 72 minutes as Stefan Scepovic poked home Efe Ambrose's header, the Nigerian powering a Johansen corner towards goal before the Serb applied the finishing touch.
There was still time for Commons to see a fourth attempt saved by Samson, but it mattered little as Celtic – who still have a game in hand on Aberdeen – closed the gap at the summit.