The striker, who turned 24 on Monday, has endured a year of frustration on the sidelines with a host of setbacks but marked his first start of the season with two goals at Bramall Lane.
Andy Gray also scored twice as Neil Warnock's Coca-Cola Championship side halted a slide of just one victory in six attempts.
Dario Gradi's men, however, did not provide testing opposition and have still not won since striker Dean Ashton left for Norwich in January.
Hopes of turning around their relegation form could now lie with Michael Higdon, who was also making his first start of the season, and lashed wide in the fourth minute on the fringe of the six-yard area with his back to goal.
But Warnock's side looked more threatening as they attacked, with Andy Liddell volleying over a minute later after positive work from Kabba on the left.
Kabba opened the scoring in the 14th minute when he was fed on the edge of the area by Gray, turned superbly and hit a well-directed shot just inside Ben Williams' far post.
Although the home side were the ascendancy, Higdon came close for the Railwaymen in the 20th minute when he forced Paddy Kenny into a low save.
Strike-partner Mark Rivers found him with a teasing through-ball, and Blades stopper Kenny had to collect at the second attempt as Rivers homed in on goal.
On the half-hour mark Kabba had another effort on goal after chasing a decent long ball from Alan Quinn, with his shot lacked power this time.
But the 16,079 crowd - the lowest league attendance of the season at Bramall Lane - were not made to wait long for the second goal.
In the 39th minute the lead was extended as Gray slid in neatly at the near post to finish from Liddell's low cross from the right.
The Blades looked to extend their lead after the restart, with Liddell volleying over and Phil Jagielka storming into the penalty area and drilling a low cross in front of Williams' goal.
Kabba was a constant menace to Crewe's defence - who had Colin Murdock and Stephen Foster returning - and his dangerous run and cross just evaded Gray in the 55th minute.
In the 66th minute Kabba added the third, smacking home a volley into the far post after Liddell's intelligent back-heel sent the striker into the penalty area and beyond the visitors' defence.
Warnock brought Kabba off a minute later, with the sparse crowd giving him a standing ovation.
Substitute Danny Cadamarteri hit the post with 17 minutes remaining, and two minutes later Gray notched the fourth, stabbing home at the second attempt from Liddell's cross.
There could have been a fifth goal, with Liddell forcing Williams into a save with a powerful drive in the dying stages.