Rak-Sakyi, on loan from Crystal Palace, celebrated turning 22 with a goal in either half at Bramall Lane as United extended their unbeaten league start to nine matches.
The Hatters, relegated from the Premier League along with the Blades last season, slipped to their fifth league defeat of the season and sit one point above the relegation zone.
Burnley missed the chance to go top after they were held 0-0 at home by Preston in a bad-tempered Lancashire derby, with referee Gavin Ward brandishing seven yellow cards.
Preston's Emil Riis had an early effort disallowed for offside, which TV replays showed to be the wrong decision.
West Bromwich Albion's winless league run extended to three matches as they were held to 0-0 by Millwall at The Hawthorns.
Norwich maintained their climb up the table and extended their unbeaten home league run to 20 matches by thumping Hull 4-0 at Carrow Road.
Plymouth boss Wayne Rooney was sent off in his side's 2-1 home win against Blackburn as Morgan Whittaker scored a stoppage-time winner.
Former Manchester United star Rooney was shown a red card in the second half for protesting after Blackburn defender Joe Rankin-Costello's late header had cancelled out Michael Obafemi's first-half opener.
Whittaker headed a dramatic late winner to ensure Rooney still ended the day on a high.
Kwadwo Baah's late goal sealed Watford a 2-1 home win against Middlesbrough after Edo Kayembe had cancelled out George Edmundson's opener for the visitors.
Louie Sibley's first goal for Oxford denied Portsmouth their first win of the season in a 1-1 draw.
Portsmouth boss John Mousinho later apologised to assistant referee Bhupinder Singh Gill after the game had been temporarily halted in the second half for an alleged discriminatory comment made from the stands.
Sheffield Wednesday's Shea Charles fired a stoppage-time winner to clinch his side a 2-1 victory at Coventry.
Derby won 2-0 at home against QPR, while Swansea were held 0-0 at home by Stoke.
