Kyle Lafferty came off the bench to score twice and provide an assist as Northern Ireland left it late to put 10-man San Marino to the sword in a 4-0 World Cup qualifying win at Windsor Park.
Although they dominated the Group C contest and created a string of chances, Michael O'Neill's side struggled to build upon Davis' opener, which arrived from the spot after 26 minutes.
It was not until 11 minutes from time that they doubled their advantage when Lafferty slotted home a Shane Ferguson cross and the Norwich City striker then teed up Jamie Ward to add the third from close range.
Lafferty duly completed his influential cameo by making it 4-0 deep into stoppage time, volleying into an empty net after fine approach work from Davis.
San Marino, meanwhile, never suggested that they were capable of securing a first win in World Cup qualifying and their cause was not helped when they lost Mirko Palazzi to a senseless second yellow card three minutes into the second half.
Pierangelo Manzaroli's men were grateful to goalkeeper Aldo Junior Simoncini for ensuring that their second successive defeat of the campaign was not a far more emphatic one.
The result maintained Northern Ireland's impressive unbeaten home record that dates back over three years, but they will face a far sterner test on Tuesday when they take on World Cup holders Germany in Hanover.
Stuart Dallas should have given the hosts the lead after four minutes, but the Leeds United midfielder somehow contrived to miss the target as he slid in to meet Niall McGinn's cross at the far post.
Josh Magennis, meanwhile, had rather surprisingly been selected to start ahead of Lafferty, Northern Ireland's top scorer during their successful Euro 2016 qualifying campaign.
That decision initially appeared justified, however, when the Charlton Athletic striker played a key role in his side's opening goal.
He was pulled back by San Marino skipper Alessandro Della Valle as he tried to reach a Ferguson delivery from the left and Davis made no mistake with the resulting penalty.
Davis should have claimed his and Northern Ireland's second goal just before the break, firing wastefully wide after being teed up by Ward, who himself then saw a header kept out by Simoncini.
In a lively opening to the second half, Ward was again foiled by Simoncini, this time after firing in a volley from the edge of the box.
And San Marino then found themselves reduced to 10 men when Palazzi, who had been booked for a foul on McGinn in the first half, collected another caution for needlessly impeding Michael McGovern as the home goalkeeper attempted to launch a counter-attack with a long throw.
Simoncini continued to keep his side in the game with a fine solo display, twice denying McGinn and also blocking well-struck efforts from Ward and Magennis as the home side piled on the pressure.
He was helpless to keep out Lafferty in the 79th minute, however, after the substitute got ahead of his marker to meet another fine cross from the impressive Ferguson.
Lafferty then claimed an assist as his downward header from Ferguson's cross fell kindly for Ward, who applied the finish at the back post.
And the 29-year-old still had time to make one final further contribution as he gleefully slammed home Davis' clever chipped cross right at the death.