A minute later Lawrie Dudfield came close to doubling the lead when he raced on to Underwood's backpass on the edge of the box, but put his shot wide with the 'keeper just in front of him.
Alexander nearly had his second 10 minutes later when he got between the defender and the goalkeeper, but Turley saved with his legs.
The City forward had a penalty appeal turned down in front of the South Stand on the half-hour mark with Turley clashing with him inside the box, but the referee waved play on.
David Beresford was then substituted with a calf/hamstring injury. Andy Holt replaced him on the left flank.
Wardley headed way over when he found himself free at the back post from Hall's cross.
Five minutes later Musselwhite made a great stop from Partridge when the Rushden forward got through on goal.
Brian Talbot made two changes at half time, bringing on Jon Brady and ex-Tiger Duane Darby.
Onandi Lowe wide shot was the only action of note early in the second half.
Jason Van Blerk was booked, before Justin Whittle replaced the struggling Richard Sneekes on the hour.
Things boiled over minutes later when Lawrie Dudfield was pulled back by the last man. On the linesman's advice the referee gave a free kick, which Turley saved from Alexander, but jeers surrounded the stadium as the man in black didn't even speak to Tillson who should have been sent off by the laws of the game.
However, 7 minutes later Van Blerk was sent from the field for a second yellow card. Matt Wicks caught Harsley with a trailing leg after Musselwhite had collected the ball. The referee pointed to the spot and Van Blerk took his protest too far for Mr. Cowburn's liking and the yellow card was followed by a red. Cowburn has now sent off 10 players in the 22 matches he's officiated this season.
Ritchie Hanlon stepped up to take the penalty, and hit it straight down the middle as Musselwhite dived to the side.
There was a nervy finish, and Lee Philpott was brought on to shore things up.
Alexander almost sealed things in the 83rd minute as he crashed a shot from the corner of the area onto the bar.
But the visitors couldn't find an equaliser and now drop out of the play-off zone.
Plymouth stay top after beating Mansfield, with Friio scoring five minutes from time. The Stags drop out of the automatic promotion places to 4th.
Rochdale go 3rd after beating 2nd-placed Luton. City are level on points with Mansfield, and we are both a point behind Rochdale who have played 32 games. Town have three games in hand of us, and two in hand of 'Dale.
Scunthorpe are in 6th, five points behind us but have played one game less. The Iron won 1-0 today with a last-minute strike sealing victory against Oxford at Glanford Park.
Shrewsbury are 7th after drawing 3-3 at Darlington, while Rushden & Diamonds' inferior goal difference means they go down to 8th.
Cheltenham - who won 2-0 at Exeter today - are 9th and have only played 29 matches. If they win all of their games in hand then they could be challenging for automatic promotion. Kidderminster and Hartlepool are still knocking on the door of the play-offs in 10th and 11th place respectively.
To see the latest league table in full click here.