Dike’s brace followed up Cauley Woodrow’s first-half penalty, with Uche Ikpeazu grabbing a late consolation for the hosts.
The victory for Valerien Ismael’s side re-established their five-point lead over seventh-placed Bournemouth in the race for the play-offs, while the Chairboys were pushed a little bit nearer to relegation.
The Tykes will, however, have to do without their captain Alex Mowatt for the next three matches, after he was sent off for a poor challenge with his side already 2-0 up.
Both teams had a few chances to cause problems at set-pieces in the early stages, but a tame header by Ryan Tafazolli from Joe Jacobson’s corner was the best either could muster.
The first opportunity from open play came for the visitors after 19 minutes when the ball was worked out to the right for Dominik Frieser, whose effort across goal was kept out by David Stockdale.
Frieser soon had another opening after getting away from Tafazolli, but could only blaze over the bar, as Barnsley began to look more dangerous.
They were only fleeting moments of quality, however, as the game descended into an untidy scrap.
Just when it looked as though the rest of the half was going to pass by without incident, the Tykes were awarded a penalty when Tafazolli was judged to have tugged back Michal Helik in the area.
Woodrow made no mistake from the spot, shooting into the bottom corner to give Barnsley a half-time lead at the end of a forgettable first 45 minutes.
They went on to double that advantage in the early stages of the second half, as Frieser’s cross was headed back across goal by Mads Andersen and Dike was on hand to nod in from close range.
Stockdale tried to catch his opposite number Brad Collins off-guard with a free-kick from just inside his own half, but his audacious effort drifted wide.
Mowatt gave the Chairboys a bit of a boost in the 73rd minute by getting himself sent off for a reckless two-footed lunge on Wycombe substitute Scott Kashket.
But the depleted Tykes made absolutely sure of the victory with nine minutes left when Dike swept in Callum Brittain’s cross with a first-time finish at the near post.
Wycombe did pull a goal back in the 85th minute as Garath McCleary’s cross found its way to Ikpeazu at the back post and the striker finished well.
A late flourish from the hosts was too little, too late, but they did come close to a second right at the end of stoppage time as Adebayo Akinfenwa’s shot was pushed away by Collins.