Boro were outplayed for large periods of a low-key encounter, but goals from Chris Killen and Jonathan Franks extended the club's unbeaten home run to nine matches and lifted them to eighth position in the Championship.
They've closed to within five points of Cardiff City in the final play-off position, although the Bluebirds can extend that gap when they entertain Sheffield United tonight.
Preston were cursing their misfortune yesterday evening after Ross Wallace cracked a second-half strike against the post and referee Steve Tanner denied Darren Carter what appeared to be a certain penalty, but after his prematch plans were thrown into chaos by the outbreak of a virus, Strachan felt his side had earned their lucky breaks.
We've had a traumatic couple of days with injuries, illness and the rest of it, said the Boro boss. The team got changed three or four times before kick-off because a number of bodies were ill or unfit.
The victory had nothing to do with football, but it had a lot to do with drive, determination and a will not to get beat. It wasn't beautiful to watch, that's for sure, and Preston must be feeling unfortunate they've got beat.
But this game is the first one since I came where I can say we've had a real bit of luck.
Killen's 29th-minute header followed Saturday's strike against Reading, and made it three goals in 11 starts since the New Zealand international joined on loan from Celtic.
Killen has spoken of his desire to earn a permanent contract at the Riverside, and Strachan admits the striker is making an increasingly compelling case.
He can't do much more than score, he said. I think he's a guy who hasn't played regularly for two years, and the more games he plays, the better he will become.
Strachan also praised much-maligned goalkeeper Brad Jones, who followed Saturday's impressive display with another solid showing.
between the sticks.