The Southampton pair each grabbed first-half assists as the Young Lions roared into a two-goal lead inside the opening 45 minutes in Milton Keynes.
The hosts dominated proceedings at stadiummk throughout, especially so after Finland had been reduced to ten men midway through the second half.
And their third goal arrived in injury time as West Brom striker Saido Berahino scored his second of the evening in stoppage time.
Shaw and Ward-Prowse were both named in Gareth Southgate’s starting XI, with Ward-Prowse collecting his fifth caps and Shaw his third.
Left-back Luke created a half-chance for the Young Lions after only five minutes at stadiummk, playing a one-two with Liverpool’s Raheem Sterling before flashing a low centre across the face of goal.
Ward-Prowse’s set-pieces have become something of a trademark during his games for Saints this season, and it was from one of his free-kicks that England took the lead.
With 22 minutes gone, the 19-year-old sent over a whipped delivery from the left flank that was headed in at the back post by Michael Keane for 1-0.
The hosts continued to dominate the opening period, and duly found a second eight minutes from the break – and Shaw had a major hand in the goal.
The Southampton man beat two opponents down the left before firing in a low shot that was spilled by Finland goalkeeper Jesse Joronen, but striker Berahino was on hand to bundle in.
Ward-Prowse saw a free-kick frantically punched clear just before the interval, while Joronen spilled one of Shaw’s low crosses four minutes into the second half.
The visitors were reduced to ten men 20 minutes from time when defender Patrick O’Shaughnessy was dismissed for a second bookable offence having clattered into Shaw.
The left-back was close to getting a second assist on 79 minutes when his low cross was dummied by substitute Will Hughes but Berahino could only curl his shot onto the crossbar.
Ward-Prowse almost scored his second international goal a minute from time as he curled free-kick towards goal from 25 yards, but his effort went inches wide.
Instead it was Berahino who rounded off a good evening's work when he side-footed home on 90 minutes after good work by substitute Jesse Lingard.
England Under-21s: Jack Butland, Carl Jenkinson, John Stones, Michael Keane, Luke Shaw, Nathaniel Chalobah (Will Hughes 64), James Ward-Prowse, Ravel Morrison (Jesse Lingard 83), Wilfried Zaha, Raheem Sterling (Tom Ince 65), Saido Berahino. Unused substitutes: George Long (GK), Jack Robinson, Eric Dier, Danny Ings.