Jonathan Woodgate's side have now won all four of their matches during the Christmas programme, alleviating their relegation worries and enabling them to start looking upwards towards the play-off places.
Preston, on the other hand, are stuck in a rut, with their latest defeat coming courtesy of an insipid performance that saw them fail to match Middlesbrough in all areas of the field.
Boro ended 2019 in impressive fashion, winning 2-0 at promotion-chasing West Brom, and the Teessiders picked up where they had left off as they dominated the opening stages at Deepdale.
Marvin Johnson drilled an early strike narrowly wide of a post, and was involved again moments later as he sent a cross from the left-hand side that Gestede glanced wide under pressure from two defenders.
Gestede was making his first league start of the season and was the focal point for most of Middlesbrough's attacking play. The former Blackburn striker won a number of headed knock-downs, but his strike partner, Ashley Fletcher, tended to be too far away to take advantage.
Boro were most threatening when they were able to deliver towards Gestede in the box, and the striker went close midway through the first half as he nodded Djed Spence's centre wide of the target.
Preston had not fashioned a single opportunity at that stage, and Alex Neil's side's lack of conviction was no doubt a reflection of their failure to win seven of their previous nine matches.
Paul Gallagher whistled a long-range effort wide of the target, but that was a rare moment of excitement for the hosts, who deservedly fell behind five minutes before the break.
Paddy McNair whipped a free-kick into the box, Preston's defenders failed to clear their lines, and when Marcus Tavernier nodded the ball down, Gestede was on hand to swivel and guide home a hooked overhead volley.
Preston's players increased the tempo of their play as they chased an equaliser after the interval, and Andrew Hughes went close when he nodded Ben Pearson's cross wide shortly before the hour mark.
Gestede threatened to double Middlesbrough's advantage at the other end, glancing narrowly wide from a corner, but it was Preston's Davies who was the key figure when the visitors did eventually extend their lead in the 62nd minute.
Chasing back towards his own goal with Fletcher for company, Davies panicked and prodded the ball past his own goalkeeper, Declan Rudd.