But for an injury-time display of football fireworks, the Everton boss could easily have been ruing a host of missed chances as his lacklustre side almost allowed a poor Birmingham City team to salvage a draw.
Everton welcomed Birmingham to Merseyside after an impressive seven-day period that saw them halt their league slide, top their UEFA Cup group and make the quarter-finals of the Carling Cup.
Birmingham, for their part, arrived on the back of a decent win last week against Wigan that saw Steve Bruce's men halt a five-game losing streak.
Early on it became apparent that the Midlands side has come to Goodison not to lose, rather than aiming for a win, as the five-man midfield offered little in the way of service to lone striker Cameron Jerome.
The first real chance of the game came on eight minutes when Joseph Yobo slid in a second too late to convert Steven Pienaar's carefully-placed cross.
But Everton went ahead two minutes later when Yakubu finished-off a move that saw Mikel Arteta clip a cheeky pass to Pienaar, who ran into Maik Taylor's 18-yard area to supply the Nigerian with an inch-perfect pass to tuck home.
Indeed Birmingham's threat was almost non-existent in the first half, apart from a deflected long-range effort from Rafael Schmitz and a shot from Olivier Kapo which gave keeper Tim Howard little trouble.
After the goal, Everton continued to threaten only sporadically with South African Pienaar the main spark in attack.
Everton had chances to wrap-up the game in the first half, but by half-time the match had a tired feel and it seemed the Toffees had a lot to chew-over in the dressing room.
Yakubu almost doubled the home team's advantage in the opening minutes of the second period as his shot across goal from the deadball line rolled agonisingly wide.
Tim Cahill headed straight at the keeper a minute later and it seemed the Goodison outfit had stepped up a gear.
In the 53rd minute Birmingham brought on Garry O'Connor with Bruce switching to a straight 4-4-2 formation to try and wrestle something from the game and they immediately looked more threatening.
The Toffees appeared a little rattled as City started to gain possession in more advanced areas, though it was clear the real threat was still coming from Moyes' men.
Leon Osman, Arteta and Pienaar again all made futile attempts on Taylor's goal.
When Birmingham's equaliser arrived it was through a simple corner kick which substitute Gary McSheffrey whipped-in with pace for Kapo to rise and nod in.
Amazingly that seemed to light Everton's touch paper and, when the game was in injury time, Liam Ridgewell's clearance rolled into the path of Lee Carsley on the edge of Taylor's area.
The midfielder took one touch to control the ball and than unleashed an unstoppable drive that sent the home fans into raptures.
Forty-eight seconds later James Vaughan put the result beyond doubt when he tucked away Carsley's long headed return ball to finish the affair with a real bang.