Christiansen gave full debuts to three of the club’s new signings in goalkeeper Felix Wiedwald, centre-back Matthew Pennington and winger Ezgjan Alioski.
But it was Academy graduate Phillips who gave United a dream start after just seven minutes from a Pablo Hernandez corner.
Bolton offered little apart from an aerial threat at corners and United doubled their lead through a fine goal converted by Wood after half an hour.
Kemar Roofe raced to the byline and produced an inviting cross which was nodded on by Alioski to Wood who produced a clinical finish in off the bar.
But United’s evening took a turn for the worse in the 38th minute when Gaetano Berardi was stretchered off with a dislocated shoulder.
Bolton were continuing to threaten from set pieces and three minutes later the hosts pulled a goal back when Gary Madine firmly converted a Josh Vela corner with a powerful header.
Yet amazingly Leeds netted their third of their game just three minutes later as Phillips bagged his second.
Bolton thought Wood was offside as the New Zealand international latched on to Eunan O’Kane’s through ball but the flag stayed down and Wood fed Phillips who had an open goal to restore United’s two-goal cushion.
United then should have had a fourth in first half stoppage time but Alioski somehow put Roofe’s inviting cross over the bar from close range.
Leeds then continued to pour forward after the break with Alioski almost converting another fine Roofe cross.
But Leeds then lost centre-back Matthew Pennington to injury and within three minutes of coming on, his replacement Conor Shaugnessy conceded a penalty for a foul on Madine.
Adam Le Fondre blasted the ball home to make it 2-3 but Leeds were then denied by the crossbar just one minute later as Hernandez let fly from 20 yards.
Both sides then pushed to net the game’s sixth goal but United held firm to see out nearly eight minutes of added time to notch a thrilling victory in Christiansen’s first game in charge.
Leeds United: Wiedwald, Ayling, Pennington (Shaughnessy 64), Cooper, Berardi (Anita 38), O’Kane, Phillips, Roofe, Hernandez, Alioski (Sacko 85), Wood. Subs not used: Green, Saiz, Klich, Ekuban.
Bolton: Howard; Dervite, Wheater (Burke 53), Beevers; Darby (Armstrong 84), Vela, Cullen, Karacan (Buckley 64), Taylor; Le Fondre, Madine. Subs not used: Alnwick, Robinson, Derik, Wilbraham.
Referee: Simon Hooper.
Attendance: 19,858 (4,832 from Leeds)