For Aston Villa, an overdue drama-free outing as Unai Emery’s side cruised into the Carabao Cup fourth round courtesy of a Tammy Abraham double and a Ross Barkley header.

Unfortunately for Coventry, it was a sorry case of more of the same. Frank Lampard’s side have lost five of their six matches in all competitions and continue to leak soft goals. It was hard to know whether Abraham’s tap-in or Barkley’s free header, both from corners, was worse from a Coventry perspective. The sight of Lampard hunched in the dugout, hands clasped, has become a familiar sight.

These teams came into this game in search of a much-needed lift, both Coventry and Villa winless in the Premier League. Lampard’s side, who have lost their opening four matches by an aggregate of 10-0 and on Saturday visit Nottingham Forest hoping for lift-off, have only scored this season in this competition. Victor Torp’s sweet free-kick from the edge of Villa’s 18-yard box, to cancel out Abraham’s first goal of the season, represented Coventry’s first goal since Torp capped the scoring at Plymouth in the previous round.

This was the first competitive meeting between these sides since 5 May 2001, when Coventry’s 34-year stay in the top flight came to an end after defeat at Villa Park. They may be peers now they are back together in the same division but, despite Coventry’s £130m summer spend, in some ways they remain in different leagues. Villa handed Ibrahim Mbaye, a £47m buy from Paris Saint-Germain, and Matteo Ruggeri, a £17m purchase from Atlético Madrid, their first starts, while there was a full debut for Taylor Harwood-Bellis, the £25m arrival from Southampton. Attempting to close the gap has so far proved a thankless task.

Lampard made nine changes from Sunday’s bruising 5-0 defeat by Brighton but when Aurèle Amenda limped off through injury on 10 minutes, Bobby Thomas, wearing the captain’s armband, was the only player left from their previous starting XI. Emery made seven changes himself and George Hemmings, one of those to keep their place, was the architect for Villa’s opener, Abraham coolly rolling the ball past Dan Bentley. Ruggeri fed Hemmings down the left and the 19-year-old sent a sumptuous pass into Abraham with the outside of his right boot.

Coventry struggled to retain possession and Villa were enjoying themselves, exchanging crisp, clean passes. But then Barkley was penalised for fouling Caleb Yirenkyi on the edge of the Villa box and Torp stepped up to lift the subsequent free-kick over the Villa wall. John McGinn, the Villa captain reduced to the role of draught excluder, picked himself up from the turf. Suddenly Coventry were full of confidence, a little giddy even. Thomas moonlighted as a striker, forcing an error from Tyrone Mings but then declined a golden opportunity to shoot at goal and the chance fizzled out. Gustavo Hamer then sent a left-foot shot just past the Villa upright.

Coventry were reborn but Villa responded. McGinn spurned a decent chance for Villa, drilling a first-time shot into the side-netting. McGinn smacked his hands together in frustration. A few minutes later Barkley sent a low drive at goal that Bentley did well to push wide for a corner, from which Villa prospered. Mbaye’s inswinging delivery was on the money and Barkley, totally unmarked in the six-yard box, headed in at the front post to regain Villa’s lead.

Coventry had the meanest defence in the Championship last season but have been porous since promotion. More slack marking enabled Villa to extend their lead from another corner. McGinn, presumably heartened by an ovation from the sold-out away end behind him, whipped the ball into the six-yard box and Abraham prodded in after walking off his marker, the 18-year-old Coventry debutant Stephen Mfuni, who this month joined on loan from Manchester City.

Abraham’s second gave Villa welcome breathing space. Emery, whose side visit Tottenham on Saturday, felt comfortable enough to withdraw McGinn and Mbaye, Emi Buendía and £52m club-record signing Johan Manzambi arriving in their places. Zion Suzuki replaced the injured Marco Bizot in goal at half-time. Nicolas Jackson replaced Abraham with 69 minutes on the clock.

Villa could afford to relax if not fully recline, victory safely stowed. Up in the directors’ box, the Coventry owner, Doug King, legs crossed, looked on pensively. Lampard stewed in the home dugout. Four months on from promotion, it is amazing how quickly the mood music can change.