Wayne Rooney’s side are still 11 from safety after a 21-point deductions this season
Solanke struck 22 minutes from time in a 3-0 win over 10-man Cardiff on Thursday evening which left the club four points clear of second-placed Fulham, although having played two games more.
Ryan Christie had fired the leaders into a 25th-minute lead with the help of a deflection off defender Mark McGuinness, and the Bluebirds’ hopes of fighting their way back into the game were dealt a blow in first-half stoppage time when Leandro Bacuna was dismissed for a poor challenge on Philip Billing.
Solanke, who had set up Christie for the opening goal, extended the Cherries’ lead after Billing had cheekily back-heeled him in on goal with 68 minutes gone, and it was 3-0 seven minutes from time when Jefferson Lerma’s close-range effort went in off keeper Alex Smithies.
There was late drama at Ashton Gate as defender Yoann Barbet headed promotion-chasing QPR to a 2-1 comeback victory over 10-man Bristol City.
Alex Scott got City off to the perfect start when he fired them ahead with just three minutes gone, but the visitors were level in added time before the break when Charlie Austin struck from the penalty spot after Luke Amos has been brought down by Cameron Pring.
The home side’s woes deepened 11 minutes after the restart when Andy King was sent off for a second bookable offence after hauling back Rangers’ skipper Stefan Johansen, whose late cross was headed home by Barbet to snatch the points.
Rangers, egter, remain a point behind sixth-placed Huddersfield after Duane Holmes’ lone strike inflicted a second successive defeat on Nottingham Forest.
The visitors went ahead on the half-hour when Holmes controlled Harry Toffolo’s driven cross and fired home.
Forest returned in determined mood after the break with Brennan Johnson twice going close and Lewis Grabban and Philip Zinckernagel also threatening, but Town held out to secure a third win on the trot.
That feat was matched by bottom-of-the-table Derby, but only after more late heroics from substitute Colin Kazim-Richards.
Luke Plange had handed the Rams an early lead when he ran on to Kamil Jozwiak’s through-ball and beat keeper Adam Davies, but Tom Ince came off the bench to drag the Potters back into it with 12 minutes remaining.
Egter, the visitors were not to be denied and 35-year-old Kazim-Richards, who had fired them to victory over West Brom on Monday, once again claimed all three points with an 85th-minute winner to drag Derby, who have been docked 21 points this season, to within four of second-bottom Barnsley.