Rafa Benitez has long come to accept the fact that he will leave Stamford Bridge in May unloved, unheralded and unlamented but, whatever happens between now and then, he will always have 1 April.

Today was the standout result of Benitez's largely unhappy 17 weeks in charge of a club that has descended into recrimination and rage since his appointment – and if he wanted reassurance of the significance of beating Manchester United in the FA Cup, it was the fact that he was spared his usual abuse.

At the final whistle, Benitez tugged his jacket around him, shook Sir Alex Ferguson's hand for the second time that afternoon and left Stamford Bridge to its own celebrations. After losing to Southampton on Saturday, being allowed to slip away was far preferable to the consequences of another defeat. In recent years, Chelsea have, in the modern parlance, owned the FA Cup, so a place in the semi-finals against Manchester City on 14 April is the very least the support expect.

This Chelsea team, which had six changes from the side that lost at St Mary's, did not overrun United, but in the moments that really mattered – those moments when the finesse of the really top players tells – it was Chelsea who prevailed. Those two occasions were Demba Ba's expertly taken goal shortly after half-time and then Petr Cech's save from Javier Hernandez just after the hour.

It has been a strange season at Chelsea, even by their own very high standards in that category, but the feeling today was that this team has the potential to challenge next season. Eden Hazard and Oscar will have another season under their belts; Juan Mata gets better and better; and if they can just find another striker and some poor soul to manage the team then there could yet be a title challenge.

In the meantime they have to contemplate the price of victory. First of all, an injury to Ashley Cole, whose hamstring gave out as he went through the gears in a chase with Danny Welbeck down the wing in the first half. Secondly, there is the prospect of fixture congestion if they reach the Europa League semi-finals, including the possibility of having to play 15 games in 45 days, starting on Thursday, to the end of the season.

Once again, Benitez will be forced into making tough choices about his team selections as the big games come relentlessly in the last seven weeks of the season. He knows that every Chelsea manager's priority is to ensure the team's participation in the Champions League, yet the prospect of winning the Europa League or the FA Cup, or both, will be sorely tempting for a manager besieged on all sides.

Yesterday, he unleashed the first string on United, which meant Frank Lampard and John Terry were on the bench, while Ferguson made seven changes from the side that beat Sunderland on Saturday. There was no Wayne Rooney again – he has a groin problem that should be resolved in time for the Manchester City game on Monday. Robin van Persie was a substitute who could not change the game when he came on.

It is nine appearances for Van Persie now without a goal and, as for United, they find themselves in a strange kind of limbo. They are strolling to the league title and, although it would be very nice for them to beat City on Monday, there is not the imperative to do so. In many respects this has been a great season for them, and when they look back on it they will see it that way, but at the moment there is the inescapable sense that it could have been better.

It would not have taken a vintage performance from United to win this game but in the end they did not come close. Rio Ferdinand was just a fraction too late getting tight to Ba when Mata picked him out with a clever ball into the area and the striker took it on the full, guiding rather than blasting it past David de Gea, who had no chance at all.

All in, it was a poor Cup tie between two sides who looked set on doing the least possible required to win the game. Hernandez's header from Welbeck's ball to the back post was heading in the opposite direction to Cech's dive but he managed to readjust and make the save brilliantly. Van Persie had a late chance from Patrice Evra's cross that he could not keep on target.

In the first half, Welbeck had looked the pick of United's side, switching from a central role behind Hernandez, to out on the right wing, where he encountered Cole. He, like many of his team-mates, faded in the second half. Out on the left wing, Tom Cleverley looked very far from the parts of the pitch where he can exert influence. Michael Carrick also struggled after the break.

When Ferguson cast around for an option to jolt his side back into life it was Ryan Giggs to whom he eventually turned. Giggs' ball to Hernandez that eluded David Luiz was crossed back in by Antonio Valencia but Van Persie failed again with the header. Otherwise United felt strangely flat, even in those final stages when they were fighting to stay in a competition they have not won now in nine seasons.

At the start of the match, as he waited for Benitez, Ferguson made a point of shaking Lampard's hand – an interesting moment, given the latter's free agent status in the summer. The United manager identified Valencia as the only player who had lived up to the standards expected of him, along with, he said, Phil Jones, in the early stages of the game.

Ferguson could not ignore the fact that the instinct that has turned United this season into the "killing machine" – as Joe Hart memorably described them – was badly missing. They could not raise their game above mediocre against opponents who were not playing at the height of their ability either.

Yet as ever with the modern FA Cup, the big issues lie elsewhere, most notably league titles and Champions League qualification. These days, managerial careers do not live or die by their FA Cup performances but Benitez is only too aware that if he wins one, it will be another bulwark against those who would seek to diminish him.

Substitutions: Chelsea Bertrand (Cole, 21), Moses (Oscar, 90), Torres (Ba, 90). Man Utd Van Persie (Cleverley, 61), Giggs (Nani, 65), Young (Welbeck, 80). Booked: Chelsea Bertrand, Azpilicueta, Mata, Oscar. Man Utd Cleverley.

Man of the match Mata. Match rating 6/10.

Possession: Chelsea 44%. Man Utd 56%.

Attempts on target: Chelsea 5. Man Utd 2.

Referee P Dowd (Staffordshire).

Attendance 40,704.

FA Cup semi-final draw

13 April Millwall v Wigan

14 April Chelsea v Man City

Both ties to take place at Wembley

Deja vu Demba: Ba's carbon-copy strikes

As Sir Alex Ferguson pointed out, Demba Ba's superb goal was almost a carbon copy of his strike for Newcastle United in the 3-0 win over Ferguson's side on 4 January 2012.

On that occasion, after picking up Shola Ameobi's knock-down, Ba hooked the ball past Anders Lindegaard into the far corner under pressure from Rio Ferdinand. The same defender got on the wrong side of Ba yesterday after Juan Mata's superb lofted pass and could only look on as the same outcome unfolded.